As the light is incident at a glass–air boundary with an angle less than the critical angle, total internal reflection does not occur at that surface. To mitigate this problem, a mirror coating is used on those sufaces. Typically an aluminum mirror coating reflectivity of 87% to 93%) or silver mirror coating (reflectivity of 95% to 98%) is used. The transmission of the prism can be improved by using a dielectric coating rather than a metallic mirror coating. This causes the prism surfaces to act as a dielectric mirror. The dielectric multilayer coating increases reflectivity from the prism surfaces by acting as a distributed Bragg reflector. A well-designed dielectric coating can provide a reflectivity of more than 99% across the visible light spectrum. This reflectivity is much improved compared to either an aluminum or silver mirror coating and the performance of the Schmidt-Pechan prism is similar to the Porro prism or the Abbe-Koenig prism.The requirement for a mirror coating makes the Schmidt-Pechan roof prism more lossy than the other image erectors using Porro prism or Abbe-Koenig prism that rely only on total internal reflections. Phase correction The multiple internal reflections also cause a polarization-dependent phase-lag of the transmitted light, in a manner similar to a Fresnel rhomb. This must be suppressed by multilayer "phase-correction coatings" applied to one of the roof surfaces to avoid unwanted interference effects and a loss of contrast in the image.In a roof prism without a phase correcting coating s-polarized and p-polarized light each acquire a different geometric phase as they pass through the upper prism. When the two polarized components are recombined interference between the s-polarized and p-polarized light results in an different intensity distribution perpendicular to the roof edge as compared to that along the roof edge. This effect reduces contrast and resolution in the image perpendicular to the roof edge. Giving an inferior image compared to that from a porro prism erecting system. This roof edge diffraction effect may also be seen as a diffraction spike perpendicular to the roof edge generated by bright points in the image.This effect can be seen in the elongation of the Airy disk [http://www.zbirding.info/zbirders/blogs/sing/archive/2006/08/09/189.aspx] in the direction perpendicular crest of the roof as this is a diffraction from the discontinuity at the roof crest.The unwanted interference effects are suppressed by vapour depositing a special dielectric coating known as a "phase-compensating coating" on the roof surfaces of the roof prism. This coating corrects for the difference in geometric phase between s- and p-polarized light so both have effectively the same phase shift and no interference degrades the image.

Glass–air transitions All of the entry and exit surfaces must be optically coated to minimize losses, though the type of coating has to be carefully chosen as the same faces of the prism act both as entry faces (desiring good anti-reflection coating) and internally reflective faces (require a coating maximizing reflection). A paper, "Progress in Binocular Design", by Konrad Siel at Swarovski shows that single-layer anti-reflective coatings on these surfaces maximized image contrast [http://www.optics.arizona.edu/optomech/references/papers/Seil%201991.pdf] . Reflection losses As the light is incident at a glass–air boundary with an angle less than the critical angle, total internal reflection does not occur at that surface. To mitigate this problem, a mirror coating is used on those sufaces. Typically an aluminum mirror coating reflectivity of 87% to 93%) or silver mirror coating (reflectivity of 95% to 98%) is used. The transmission of the prism can be improved by using a dielectric coating rather than a metallic mirror coating. This causes the prism surfaces to act as a dielectric mirror. The dielectric multilayer coating increases reflectivity from the prism surfaces by acting as a distributed Bragg reflector. A well-designed dielectric coating can provide a reflectivity of more than 99% across the visible light spectrum. This reflectivity is much improved compared to either an aluminum or silver mirror coating and the performance of the Schmidt-Pechan prism is similar to the Porro prism or the Abbe-Koenig prism.The requirement for a mirror coating makes the Schmidt-Pechan roof prism more lossy than the other image erectors using Porro prism or Abbe-Koenig prism that rely only on total internal reflections. Phase correction The multiple internal reflections also cause a polarization-dependent phase-lag of the transmitted light, in a manner similar to a Fresnel rhomb. This must be suppressed by multilayer "phase-correction coatings" applied to one of the roof surfaces to avoid unwanted interference effects and a loss of contrast in the image.In a roof prism without a phase correcting coating s-polarized and p-polarized light each acquire a different geometric phase as they pass through the upper prism. When the two polarized components are recombined interference between the s-polarized and p-polarized light results in an different intensity distribution perpendicular to the roof edge as compared to that along the roof edge. This effect reduces contrast and resolution in the image perpendicular to the roof edge. Giving an inferior image compared to that from a porro prism erecting system. This roof edge diffraction effect may also be seen as a diffraction spike perpendicular to the roof edge generated by bright points in the image.This effect can be seen in the elongation of the Airy disk [http://www.zbirding.info/zbirders/blogs/sing/archive/2006/08/09/189.aspx] in the direction perpendicular crest of the roof as this is a diffraction from the discontinuity at the roof crest.The unwanted interference effects are suppressed by vapour depositing a special dielectric coating known as a "phase-compensating coating" on the roof surfaces of the roof prism. This coating corrects for the difference in geometric phase between s- and p-polarized light so both have effectively the same phase shift and no interference degrades the image.

Prism (optics) — For other uses, see Prism (disambiguation). A plastic prism In optics, a prism is a transparent optical element with flat, polished surfaces that refract light. The exact angles between the surfaces depend on the application. The traditional… …   Wikipedia

Porroprismbinoculars

$$\begin{align}d - f &= \frac{s\cdot f}{s - f} - f \\ &= \frac{s\cdot f}{s - f} - \frac{f(s-f)}{s-f}\\ &=\frac{f^2}{s-f}\end{align}$$

The iris is marked with some repeatable settings labelled 1-5. I can't find any documentation to tell me what the actual size of the iris is at these settings but I need to work out the NA at each one. Is there a simple way of doing this?

Problems with the Schmidt-Pechan prism Glass–air transitions All of the entry and exit surfaces must be optically coated to minimize losses, though the type of coating has to be carefully chosen as the same faces of the prism act both as entry faces (desiring good anti-reflection coating) and internally reflective faces (require a coating maximizing reflection). A paper, "Progress in Binocular Design", by Konrad Siel at Swarovski shows that single-layer anti-reflective coatings on these surfaces maximized image contrast [http://www.optics.arizona.edu/optomech/references/papers/Seil%201991.pdf] . Reflection losses As the light is incident at a glass–air boundary with an angle less than the critical angle, total internal reflection does not occur at that surface. To mitigate this problem, a mirror coating is used on those sufaces. Typically an aluminum mirror coating reflectivity of 87% to 93%) or silver mirror coating (reflectivity of 95% to 98%) is used. The transmission of the prism can be improved by using a dielectric coating rather than a metallic mirror coating. This causes the prism surfaces to act as a dielectric mirror. The dielectric multilayer coating increases reflectivity from the prism surfaces by acting as a distributed Bragg reflector. A well-designed dielectric coating can provide a reflectivity of more than 99% across the visible light spectrum. This reflectivity is much improved compared to either an aluminum or silver mirror coating and the performance of the Schmidt-Pechan prism is similar to the Porro prism or the Abbe-Koenig prism.The requirement for a mirror coating makes the Schmidt-Pechan roof prism more lossy than the other image erectors using Porro prism or Abbe-Koenig prism that rely only on total internal reflections. Phase correction The multiple internal reflections also cause a polarization-dependent phase-lag of the transmitted light, in a manner similar to a Fresnel rhomb. This must be suppressed by multilayer "phase-correction coatings" applied to one of the roof surfaces to avoid unwanted interference effects and a loss of contrast in the image.In a roof prism without a phase correcting coating s-polarized and p-polarized light each acquire a different geometric phase as they pass through the upper prism. When the two polarized components are recombined interference between the s-polarized and p-polarized light results in an different intensity distribution perpendicular to the roof edge as compared to that along the roof edge. This effect reduces contrast and resolution in the image perpendicular to the roof edge. Giving an inferior image compared to that from a porro prism erecting system. This roof edge diffraction effect may also be seen as a diffraction spike perpendicular to the roof edge generated by bright points in the image.This effect can be seen in the elongation of the Airy disk [http://www.zbirding.info/zbirders/blogs/sing/archive/2006/08/09/189.aspx] in the direction perpendicular crest of the roof as this is a diffraction from the discontinuity at the roof crest.The unwanted interference effects are suppressed by vapour depositing a special dielectric coating known as a "phase-compensating coating" on the roof surfaces of the roof prism. This coating corrects for the difference in geometric phase between s- and p-polarized light so both have effectively the same phase shift and no interference degrades the image.

Bauernfeindprism

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Monocular — For other uses, see Monocular (disambiguation). Galilean type Soviet made miniature 2.5 × 17.5 monocular …   Wikipedia

The upper prism inverts the image by three total internal reflections in the vertical plane through the roof ridge. The "roof" section of the Schmidt prism flips (reverts) the image laterally with two total internal reflections in the horizontal plane from the roof surface: once on each side of the roof. This latter pair of reflections can be considered as one reflection in the vertical plane. Both inversion and reversion together cause a 180° rotation of the image. The image's handedness is not changed. The reflection from the bottom surface of the first prism is not by total internal reflection since the light is incident at an angle less than the "critical angle". This is unlike other roof prisms like the Abbe-Koenig prism. This surface of the Schmidt-Pechan prism requires a reflective coating for this prism to be usable in practice. Problems with the Schmidt-Pechan prism Glass–air transitions All of the entry and exit surfaces must be optically coated to minimize losses, though the type of coating has to be carefully chosen as the same faces of the prism act both as entry faces (desiring good anti-reflection coating) and internally reflective faces (require a coating maximizing reflection). A paper, "Progress in Binocular Design", by Konrad Siel at Swarovski shows that single-layer anti-reflective coatings on these surfaces maximized image contrast [http://www.optics.arizona.edu/optomech/references/papers/Seil%201991.pdf] . Reflection losses As the light is incident at a glass–air boundary with an angle less than the critical angle, total internal reflection does not occur at that surface. To mitigate this problem, a mirror coating is used on those sufaces. Typically an aluminum mirror coating reflectivity of 87% to 93%) or silver mirror coating (reflectivity of 95% to 98%) is used. The transmission of the prism can be improved by using a dielectric coating rather than a metallic mirror coating. This causes the prism surfaces to act as a dielectric mirror. The dielectric multilayer coating increases reflectivity from the prism surfaces by acting as a distributed Bragg reflector. A well-designed dielectric coating can provide a reflectivity of more than 99% across the visible light spectrum. This reflectivity is much improved compared to either an aluminum or silver mirror coating and the performance of the Schmidt-Pechan prism is similar to the Porro prism or the Abbe-Koenig prism.The requirement for a mirror coating makes the Schmidt-Pechan roof prism more lossy than the other image erectors using Porro prism or Abbe-Koenig prism that rely only on total internal reflections. Phase correction The multiple internal reflections also cause a polarization-dependent phase-lag of the transmitted light, in a manner similar to a Fresnel rhomb. This must be suppressed by multilayer "phase-correction coatings" applied to one of the roof surfaces to avoid unwanted interference effects and a loss of contrast in the image.In a roof prism without a phase correcting coating s-polarized and p-polarized light each acquire a different geometric phase as they pass through the upper prism. When the two polarized components are recombined interference between the s-polarized and p-polarized light results in an different intensity distribution perpendicular to the roof edge as compared to that along the roof edge. This effect reduces contrast and resolution in the image perpendicular to the roof edge. Giving an inferior image compared to that from a porro prism erecting system. This roof edge diffraction effect may also be seen as a diffraction spike perpendicular to the roof edge generated by bright points in the image.This effect can be seen in the elongation of the Airy disk [http://www.zbirding.info/zbirders/blogs/sing/archive/2006/08/09/189.aspx] in the direction perpendicular crest of the roof as this is a diffraction from the discontinuity at the roof crest.The unwanted interference effects are suppressed by vapour depositing a special dielectric coating known as a "phase-compensating coating" on the roof surfaces of the roof prism. This coating corrects for the difference in geometric phase between s- and p-polarized light so both have effectively the same phase shift and no interference degrades the image.

So if you plot the spot radius as a function of $\frac{f^2}{s-f}$ for different values of $s$ you should get a straight line whose slope is the tangent of the numerical aperture.

Method of Operation The Schmidt-Pechan prism is a merger of the designs of the Schmidt prism and the Pechan prism.The Pechan prism is a composite of two prisms separated by an air gap. It will invert or revert (flip) the image depending up orientation of the prism but not both at the same time. By replacing the second prism in the Pechan design with a Schmidt prism the Schmidt-Pechan prism can both invert and revert the image and so act as an image rotator.The Schmidt-Pechan prism consists of two glass prisms separated by an air-gap. The second, Schmidt, prism both reverts and inverts the image but in doing so deviates the path by 45°. The first prism corrects for this delivering a beam at 45° into the Schmidt prism. The design of the first prism is such that the entrance beam and exit beam are coaxial i.e. the Schmidt-Pechan prism does not deviate the beam if centered on the optical axis.The lower prism uses one total internal reflection followed by a reflection from a mirrored surface to direct the beam into the second Schmidt prism so the orientation of the image is not changed.The upper prism inverts the image by three total internal reflections in the vertical plane through the roof ridge. The "roof" section of the Schmidt prism flips (reverts) the image laterally with two total internal reflections in the horizontal plane from the roof surface: once on each side of the roof. This latter pair of reflections can be considered as one reflection in the vertical plane. Both inversion and reversion together cause a 180° rotation of the image. The image's handedness is not changed. The reflection from the bottom surface of the first prism is not by total internal reflection since the light is incident at an angle less than the "critical angle". This is unlike other roof prisms like the Abbe-Koenig prism. This surface of the Schmidt-Pechan prism requires a reflective coating for this prism to be usable in practice. Problems with the Schmidt-Pechan prism Glass–air transitions All of the entry and exit surfaces must be optically coated to minimize losses, though the type of coating has to be carefully chosen as the same faces of the prism act both as entry faces (desiring good anti-reflection coating) and internally reflective faces (require a coating maximizing reflection). A paper, "Progress in Binocular Design", by Konrad Siel at Swarovski shows that single-layer anti-reflective coatings on these surfaces maximized image contrast [http://www.optics.arizona.edu/optomech/references/papers/Seil%201991.pdf] . Reflection losses As the light is incident at a glass–air boundary with an angle less than the critical angle, total internal reflection does not occur at that surface. To mitigate this problem, a mirror coating is used on those sufaces. Typically an aluminum mirror coating reflectivity of 87% to 93%) or silver mirror coating (reflectivity of 95% to 98%) is used. The transmission of the prism can be improved by using a dielectric coating rather than a metallic mirror coating. This causes the prism surfaces to act as a dielectric mirror. The dielectric multilayer coating increases reflectivity from the prism surfaces by acting as a distributed Bragg reflector. A well-designed dielectric coating can provide a reflectivity of more than 99% across the visible light spectrum. This reflectivity is much improved compared to either an aluminum or silver mirror coating and the performance of the Schmidt-Pechan prism is similar to the Porro prism or the Abbe-Koenig prism.The requirement for a mirror coating makes the Schmidt-Pechan roof prism more lossy than the other image erectors using Porro prism or Abbe-Koenig prism that rely only on total internal reflections. Phase correction The multiple internal reflections also cause a polarization-dependent phase-lag of the transmitted light, in a manner similar to a Fresnel rhomb. This must be suppressed by multilayer "phase-correction coatings" applied to one of the roof surfaces to avoid unwanted interference effects and a loss of contrast in the image.In a roof prism without a phase correcting coating s-polarized and p-polarized light each acquire a different geometric phase as they pass through the upper prism. When the two polarized components are recombined interference between the s-polarized and p-polarized light results in an different intensity distribution perpendicular to the roof edge as compared to that along the roof edge. This effect reduces contrast and resolution in the image perpendicular to the roof edge. Giving an inferior image compared to that from a porro prism erecting system. This roof edge diffraction effect may also be seen as a diffraction spike perpendicular to the roof edge generated by bright points in the image.This effect can be seen in the elongation of the Airy disk [http://www.zbirding.info/zbirders/blogs/sing/archive/2006/08/09/189.aspx] in the direction perpendicular crest of the roof as this is a diffraction from the discontinuity at the roof crest.The unwanted interference effects are suppressed by vapour depositing a special dielectric coating known as a "phase-compensating coating" on the roof surfaces of the roof prism. This coating corrects for the difference in geometric phase between s- and p-polarized light so both have effectively the same phase shift and no interference degrades the image.

EDIT Since your lens is connected to a CMOS sensor, the above approach will not work for you. I recommend instead that you put a point source in front of the lens at a controlled (variable) distance, and measure once again the spot size.

I am not absolutely sure that these formulas work for compound lenses... perhaps somebody can either confirm this or point out the correction that is needed.

The lower prism uses one total internal reflection followed by a reflection from a mirrored surface to direct the beam into the second Schmidt prism so the orientation of the image is not changed.The upper prism inverts the image by three total internal reflections in the vertical plane through the roof ridge. The "roof" section of the Schmidt prism flips (reverts) the image laterally with two total internal reflections in the horizontal plane from the roof surface: once on each side of the roof. This latter pair of reflections can be considered as one reflection in the vertical plane. Both inversion and reversion together cause a 180° rotation of the image. The image's handedness is not changed. The reflection from the bottom surface of the first prism is not by total internal reflection since the light is incident at an angle less than the "critical angle". This is unlike other roof prisms like the Abbe-Koenig prism. This surface of the Schmidt-Pechan prism requires a reflective coating for this prism to be usable in practice. Problems with the Schmidt-Pechan prism Glass–air transitions All of the entry and exit surfaces must be optically coated to minimize losses, though the type of coating has to be carefully chosen as the same faces of the prism act both as entry faces (desiring good anti-reflection coating) and internally reflective faces (require a coating maximizing reflection). A paper, "Progress in Binocular Design", by Konrad Siel at Swarovski shows that single-layer anti-reflective coatings on these surfaces maximized image contrast [http://www.optics.arizona.edu/optomech/references/papers/Seil%201991.pdf] . Reflection losses As the light is incident at a glass–air boundary with an angle less than the critical angle, total internal reflection does not occur at that surface. To mitigate this problem, a mirror coating is used on those sufaces. Typically an aluminum mirror coating reflectivity of 87% to 93%) or silver mirror coating (reflectivity of 95% to 98%) is used. The transmission of the prism can be improved by using a dielectric coating rather than a metallic mirror coating. This causes the prism surfaces to act as a dielectric mirror. The dielectric multilayer coating increases reflectivity from the prism surfaces by acting as a distributed Bragg reflector. A well-designed dielectric coating can provide a reflectivity of more than 99% across the visible light spectrum. This reflectivity is much improved compared to either an aluminum or silver mirror coating and the performance of the Schmidt-Pechan prism is similar to the Porro prism or the Abbe-Koenig prism.The requirement for a mirror coating makes the Schmidt-Pechan roof prism more lossy than the other image erectors using Porro prism or Abbe-Koenig prism that rely only on total internal reflections. Phase correction The multiple internal reflections also cause a polarization-dependent phase-lag of the transmitted light, in a manner similar to a Fresnel rhomb. This must be suppressed by multilayer "phase-correction coatings" applied to one of the roof surfaces to avoid unwanted interference effects and a loss of contrast in the image.In a roof prism without a phase correcting coating s-polarized and p-polarized light each acquire a different geometric phase as they pass through the upper prism. When the two polarized components are recombined interference between the s-polarized and p-polarized light results in an different intensity distribution perpendicular to the roof edge as compared to that along the roof edge. This effect reduces contrast and resolution in the image perpendicular to the roof edge. Giving an inferior image compared to that from a porro prism erecting system. This roof edge diffraction effect may also be seen as a diffraction spike perpendicular to the roof edge generated by bright points in the image.This effect can be seen in the elongation of the Airy disk [http://www.zbirding.info/zbirders/blogs/sing/archive/2006/08/09/189.aspx] in the direction perpendicular crest of the roof as this is a diffraction from the discontinuity at the roof crest.The unwanted interference effects are suppressed by vapour depositing a special dielectric coating known as a "phase-compensating coating" on the roof surfaces of the roof prism. This coating corrects for the difference in geometric phase between s- and p-polarized light so both have effectively the same phase shift and no interference degrades the image.

Schmidt pechan prismvs roofprism

Binoculars — Binocular telescopes, or binoculars (also known as field glasses), are two identical or mirror symmetrical telescopes mounted side by side and aligned to point accurately in the same direction, allowing the viewer to use both eyes (binocular… …   Wikipedia

This effect can be seen in the elongation of the Airy disk [http://www.zbirding.info/zbirders/blogs/sing/archive/2006/08/09/189.aspx] in the direction perpendicular crest of the roof as this is a diffraction from the discontinuity at the roof crest.The unwanted interference effects are suppressed by vapour depositing a special dielectric coating known as a "phase-compensating coating" on the roof surfaces of the roof prism. This coating corrects for the difference in geometric phase between s- and p-polarized light so both have effectively the same phase shift and no interference degrades the image.

In a roof prism without a phase correcting coating s-polarized and p-polarized light each acquire a different geometric phase as they pass through the upper prism. When the two polarized components are recombined interference between the s-polarized and p-polarized light results in an different intensity distribution perpendicular to the roof edge as compared to that along the roof edge. This effect reduces contrast and resolution in the image perpendicular to the roof edge. Giving an inferior image compared to that from a porro prism erecting system. This roof edge diffraction effect may also be seen as a diffraction spike perpendicular to the roof edge generated by bright points in the image.This effect can be seen in the elongation of the Airy disk [http://www.zbirding.info/zbirders/blogs/sing/archive/2006/08/09/189.aspx] in the direction perpendicular crest of the roof as this is a diffraction from the discontinuity at the roof crest.The unwanted interference effects are suppressed by vapour depositing a special dielectric coating known as a "phase-compensating coating" on the roof surfaces of the roof prism. This coating corrects for the difference in geometric phase between s- and p-polarized light so both have effectively the same phase shift and no interference degrades the image.

schmidt-pechanprismvs bak-4

Roof prism — A roof prism (also called a Dach prism) is in general any kind of reflective optical prism containing a section where two faces meet at a 90° angle. Reflection from the two faces returns an image that is flipped laterally across the axis where… …   Wikipedia

This does require you to know the focal length of the lens, and the lens to be focused on infinity. Measuring the distance to the optical center of the lens can be tricky - a zoom lens is a composite lens, and they don't always have an obvious "center". You can use the distance to the focal plane instead - that should be $s+f$ .

Reflection losses As the light is incident at a glass–air boundary with an angle less than the critical angle, total internal reflection does not occur at that surface. To mitigate this problem, a mirror coating is used on those sufaces. Typically an aluminum mirror coating reflectivity of 87% to 93%) or silver mirror coating (reflectivity of 95% to 98%) is used. The transmission of the prism can be improved by using a dielectric coating rather than a metallic mirror coating. This causes the prism surfaces to act as a dielectric mirror. The dielectric multilayer coating increases reflectivity from the prism surfaces by acting as a distributed Bragg reflector. A well-designed dielectric coating can provide a reflectivity of more than 99% across the visible light spectrum. This reflectivity is much improved compared to either an aluminum or silver mirror coating and the performance of the Schmidt-Pechan prism is similar to the Porro prism or the Abbe-Koenig prism.The requirement for a mirror coating makes the Schmidt-Pechan roof prism more lossy than the other image erectors using Porro prism or Abbe-Koenig prism that rely only on total internal reflections. Phase correction The multiple internal reflections also cause a polarization-dependent phase-lag of the transmitted light, in a manner similar to a Fresnel rhomb. This must be suppressed by multilayer "phase-correction coatings" applied to one of the roof surfaces to avoid unwanted interference effects and a loss of contrast in the image.In a roof prism without a phase correcting coating s-polarized and p-polarized light each acquire a different geometric phase as they pass through the upper prism. When the two polarized components are recombined interference between the s-polarized and p-polarized light results in an different intensity distribution perpendicular to the roof edge as compared to that along the roof edge. This effect reduces contrast and resolution in the image perpendicular to the roof edge. Giving an inferior image compared to that from a porro prism erecting system. This roof edge diffraction effect may also be seen as a diffraction spike perpendicular to the roof edge generated by bright points in the image.This effect can be seen in the elongation of the Airy disk [http://www.zbirding.info/zbirders/blogs/sing/archive/2006/08/09/189.aspx] in the direction perpendicular crest of the roof as this is a diffraction from the discontinuity at the roof crest.The unwanted interference effects are suppressed by vapour depositing a special dielectric coating known as a "phase-compensating coating" on the roof surfaces of the roof prism. This coating corrects for the difference in geometric phase between s- and p-polarized light so both have effectively the same phase shift and no interference degrades the image.

Schmidt pechan prismreview

Abbe-Koenig prism — An Abbe Koenig prism is a type of reflecting prism used to invert an image (rotate it by 180°). They are commonly used in binoculars and some telescopes for this purpose. The prism is named after Ernst Abbe and Albert Koenig.The prism is made… …   Wikipedia

The answer linked by @tmwilson26 is certainly helpful, but it may not be what you are looking for. There are a couple of different ways to approach this problem, and it depends a little bit on the equipment you have available. Note that if you have a zoom lens, leaving the iris at a fixed value will not, in general, result in a constant NA - instead the NA will depend on the focal length as well as the iris aperture.

The transmission of the prism can be improved by using a dielectric coating rather than a metallic mirror coating. This causes the prism surfaces to act as a dielectric mirror. The dielectric multilayer coating increases reflectivity from the prism surfaces by acting as a distributed Bragg reflector. A well-designed dielectric coating can provide a reflectivity of more than 99% across the visible light spectrum. This reflectivity is much improved compared to either an aluminum or silver mirror coating and the performance of the Schmidt-Pechan prism is similar to the Porro prism or the Abbe-Koenig prism.The requirement for a mirror coating makes the Schmidt-Pechan roof prism more lossy than the other image erectors using Porro prism or Abbe-Koenig prism that rely only on total internal reflections. Phase correction The multiple internal reflections also cause a polarization-dependent phase-lag of the transmitted light, in a manner similar to a Fresnel rhomb. This must be suppressed by multilayer "phase-correction coatings" applied to one of the roof surfaces to avoid unwanted interference effects and a loss of contrast in the image.In a roof prism without a phase correcting coating s-polarized and p-polarized light each acquire a different geometric phase as they pass through the upper prism. When the two polarized components are recombined interference between the s-polarized and p-polarized light results in an different intensity distribution perpendicular to the roof edge as compared to that along the roof edge. This effect reduces contrast and resolution in the image perpendicular to the roof edge. Giving an inferior image compared to that from a porro prism erecting system. This roof edge diffraction effect may also be seen as a diffraction spike perpendicular to the roof edge generated by bright points in the image.This effect can be seen in the elongation of the Airy disk [http://www.zbirding.info/zbirders/blogs/sing/archive/2006/08/09/189.aspx] in the direction perpendicular crest of the roof as this is a diffraction from the discontinuity at the roof crest.The unwanted interference effects are suppressed by vapour depositing a special dielectric coating known as a "phase-compensating coating" on the roof surfaces of the roof prism. This coating corrects for the difference in geometric phase between s- and p-polarized light so both have effectively the same phase shift and no interference degrades the image.

Now the numerical aperture is usually the $\sin$ of the angle - so if you care about the difference (which is important as NA gets larger) you need to do a bit of math:

I have a lens system made up of some components of the Leica Z16 APO zoom system. This includes a built-in iris diaphragm to adjust the Numerical Aperture (NA) and therefore the depth-of-field (DOF).

Now we can use the formula for the distance to the focal point. If the source is a distance $s$ from the lens, and the focal length is $f$, then we expect the point to come into focus at a distance $d$ where

The requirement for a mirror coating makes the Schmidt-Pechan roof prism more lossy than the other image erectors using Porro prism or Abbe-Koenig prism that rely only on total internal reflections. Phase correction The multiple internal reflections also cause a polarization-dependent phase-lag of the transmitted light, in a manner similar to a Fresnel rhomb. This must be suppressed by multilayer "phase-correction coatings" applied to one of the roof surfaces to avoid unwanted interference effects and a loss of contrast in the image.In a roof prism without a phase correcting coating s-polarized and p-polarized light each acquire a different geometric phase as they pass through the upper prism. When the two polarized components are recombined interference between the s-polarized and p-polarized light results in an different intensity distribution perpendicular to the roof edge as compared to that along the roof edge. This effect reduces contrast and resolution in the image perpendicular to the roof edge. Giving an inferior image compared to that from a porro prism erecting system. This roof edge diffraction effect may also be seen as a diffraction spike perpendicular to the roof edge generated by bright points in the image.This effect can be seen in the elongation of the Airy disk [http://www.zbirding.info/zbirders/blogs/sing/archive/2006/08/09/189.aspx] in the direction perpendicular crest of the roof as this is a diffraction from the discontinuity at the roof crest.The unwanted interference effects are suppressed by vapour depositing a special dielectric coating known as a "phase-compensating coating" on the roof surfaces of the roof prism. This coating corrects for the difference in geometric phase between s- and p-polarized light so both have effectively the same phase shift and no interference degrades the image.

Roofprismbinoculars

The unwanted interference effects are suppressed by vapour depositing a special dielectric coating known as a "phase-compensating coating" on the roof surfaces of the roof prism. This coating corrects for the difference in geometric phase between s- and p-polarized light so both have effectively the same phase shift and no interference degrades the image.

Assuming you know the focal length, and that you focused the lens on infinity (so you set $d' = f$), then your imaging plane would be away from the in-focus plane by a distance $d - f$. In the small angle approximation, the point would become a circle with a radius $r = NA\cdot (d-f)$.

The Schmidt-Pechan prism is a merger of the designs of the Schmidt prism and the Pechan prism.The Pechan prism is a composite of two prisms separated by an air gap. It will invert or revert (flip) the image depending up orientation of the prism but not both at the same time. By replacing the second prism in the Pechan design with a Schmidt prism the Schmidt-Pechan prism can both invert and revert the image and so act as an image rotator.The Schmidt-Pechan prism consists of two glass prisms separated by an air-gap. The second, Schmidt, prism both reverts and inverts the image but in doing so deviates the path by 45°. The first prism corrects for this delivering a beam at 45° into the Schmidt prism. The design of the first prism is such that the entrance beam and exit beam are coaxial i.e. the Schmidt-Pechan prism does not deviate the beam if centered on the optical axis.The lower prism uses one total internal reflection followed by a reflection from a mirrored surface to direct the beam into the second Schmidt prism so the orientation of the image is not changed.The upper prism inverts the image by three total internal reflections in the vertical plane through the roof ridge. The "roof" section of the Schmidt prism flips (reverts) the image laterally with two total internal reflections in the horizontal plane from the roof surface: once on each side of the roof. This latter pair of reflections can be considered as one reflection in the vertical plane. Both inversion and reversion together cause a 180° rotation of the image. The image's handedness is not changed. The reflection from the bottom surface of the first prism is not by total internal reflection since the light is incident at an angle less than the "critical angle". This is unlike other roof prisms like the Abbe-Koenig prism. This surface of the Schmidt-Pechan prism requires a reflective coating for this prism to be usable in practice. Problems with the Schmidt-Pechan prism Glass–air transitions All of the entry and exit surfaces must be optically coated to minimize losses, though the type of coating has to be carefully chosen as the same faces of the prism act both as entry faces (desiring good anti-reflection coating) and internally reflective faces (require a coating maximizing reflection). A paper, "Progress in Binocular Design", by Konrad Siel at Swarovski shows that single-layer anti-reflective coatings on these surfaces maximized image contrast [http://www.optics.arizona.edu/optomech/references/papers/Seil%201991.pdf] . Reflection losses As the light is incident at a glass–air boundary with an angle less than the critical angle, total internal reflection does not occur at that surface. To mitigate this problem, a mirror coating is used on those sufaces. Typically an aluminum mirror coating reflectivity of 87% to 93%) or silver mirror coating (reflectivity of 95% to 98%) is used. The transmission of the prism can be improved by using a dielectric coating rather than a metallic mirror coating. This causes the prism surfaces to act as a dielectric mirror. The dielectric multilayer coating increases reflectivity from the prism surfaces by acting as a distributed Bragg reflector. A well-designed dielectric coating can provide a reflectivity of more than 99% across the visible light spectrum. This reflectivity is much improved compared to either an aluminum or silver mirror coating and the performance of the Schmidt-Pechan prism is similar to the Porro prism or the Abbe-Koenig prism.The requirement for a mirror coating makes the Schmidt-Pechan roof prism more lossy than the other image erectors using Porro prism or Abbe-Koenig prism that rely only on total internal reflections. Phase correction The multiple internal reflections also cause a polarization-dependent phase-lag of the transmitted light, in a manner similar to a Fresnel rhomb. This must be suppressed by multilayer "phase-correction coatings" applied to one of the roof surfaces to avoid unwanted interference effects and a loss of contrast in the image.In a roof prism without a phase correcting coating s-polarized and p-polarized light each acquire a different geometric phase as they pass through the upper prism. When the two polarized components are recombined interference between the s-polarized and p-polarized light results in an different intensity distribution perpendicular to the roof edge as compared to that along the roof edge. This effect reduces contrast and resolution in the image perpendicular to the roof edge. Giving an inferior image compared to that from a porro prism erecting system. This roof edge diffraction effect may also be seen as a diffraction spike perpendicular to the roof edge generated by bright points in the image.This effect can be seen in the elongation of the Airy disk [http://www.zbirding.info/zbirders/blogs/sing/archive/2006/08/09/189.aspx] in the direction perpendicular crest of the roof as this is a diffraction from the discontinuity at the roof crest.The unwanted interference effects are suppressed by vapour depositing a special dielectric coating known as a "phase-compensating coating" on the roof surfaces of the roof prism. This coating corrects for the difference in geometric phase between s- and p-polarized light so both have effectively the same phase shift and no interference degrades the image.

Now you can repeat this measurement for different settings of the focal length of the zoom lens, and for different values of the iris setting. Note that by defocusing to various points and measuring the slope you avoid the problem of not knowing the focal length of the lens.

Half Pentaprism

Schmidt pechan prismprice

A Schmidt-Pechan prism is a type of optical prism used to rotate an image by 180°. They are commonly used in binoculars as an "image erecting system". Compared to binoculars using a Porro prism or Abbe-Koenig a binoculars using a Schmidt-Pechan roof prism is more compact. Method of Operation The Schmidt-Pechan prism is a merger of the designs of the Schmidt prism and the Pechan prism.The Pechan prism is a composite of two prisms separated by an air gap. It will invert or revert (flip) the image depending up orientation of the prism but not both at the same time. By replacing the second prism in the Pechan design with a Schmidt prism the Schmidt-Pechan prism can both invert and revert the image and so act as an image rotator.The Schmidt-Pechan prism consists of two glass prisms separated by an air-gap. The second, Schmidt, prism both reverts and inverts the image but in doing so deviates the path by 45°. The first prism corrects for this delivering a beam at 45° into the Schmidt prism. The design of the first prism is such that the entrance beam and exit beam are coaxial i.e. the Schmidt-Pechan prism does not deviate the beam if centered on the optical axis.The lower prism uses one total internal reflection followed by a reflection from a mirrored surface to direct the beam into the second Schmidt prism so the orientation of the image is not changed.The upper prism inverts the image by three total internal reflections in the vertical plane through the roof ridge. The "roof" section of the Schmidt prism flips (reverts) the image laterally with two total internal reflections in the horizontal plane from the roof surface: once on each side of the roof. This latter pair of reflections can be considered as one reflection in the vertical plane. Both inversion and reversion together cause a 180° rotation of the image. The image's handedness is not changed. The reflection from the bottom surface of the first prism is not by total internal reflection since the light is incident at an angle less than the "critical angle". This is unlike other roof prisms like the Abbe-Koenig prism. This surface of the Schmidt-Pechan prism requires a reflective coating for this prism to be usable in practice. Problems with the Schmidt-Pechan prism Glass–air transitions All of the entry and exit surfaces must be optically coated to minimize losses, though the type of coating has to be carefully chosen as the same faces of the prism act both as entry faces (desiring good anti-reflection coating) and internally reflective faces (require a coating maximizing reflection). A paper, "Progress in Binocular Design", by Konrad Siel at Swarovski shows that single-layer anti-reflective coatings on these surfaces maximized image contrast [http://www.optics.arizona.edu/optomech/references/papers/Seil%201991.pdf] . Reflection losses As the light is incident at a glass–air boundary with an angle less than the critical angle, total internal reflection does not occur at that surface. To mitigate this problem, a mirror coating is used on those sufaces. Typically an aluminum mirror coating reflectivity of 87% to 93%) or silver mirror coating (reflectivity of 95% to 98%) is used. The transmission of the prism can be improved by using a dielectric coating rather than a metallic mirror coating. This causes the prism surfaces to act as a dielectric mirror. The dielectric multilayer coating increases reflectivity from the prism surfaces by acting as a distributed Bragg reflector. A well-designed dielectric coating can provide a reflectivity of more than 99% across the visible light spectrum. This reflectivity is much improved compared to either an aluminum or silver mirror coating and the performance of the Schmidt-Pechan prism is similar to the Porro prism or the Abbe-Koenig prism.The requirement for a mirror coating makes the Schmidt-Pechan roof prism more lossy than the other image erectors using Porro prism or Abbe-Koenig prism that rely only on total internal reflections. Phase correction The multiple internal reflections also cause a polarization-dependent phase-lag of the transmitted light, in a manner similar to a Fresnel rhomb. This must be suppressed by multilayer "phase-correction coatings" applied to one of the roof surfaces to avoid unwanted interference effects and a loss of contrast in the image.In a roof prism without a phase correcting coating s-polarized and p-polarized light each acquire a different geometric phase as they pass through the upper prism. When the two polarized components are recombined interference between the s-polarized and p-polarized light results in an different intensity distribution perpendicular to the roof edge as compared to that along the roof edge. This effect reduces contrast and resolution in the image perpendicular to the roof edge. Giving an inferior image compared to that from a porro prism erecting system. This roof edge diffraction effect may also be seen as a diffraction spike perpendicular to the roof edge generated by bright points in the image.This effect can be seen in the elongation of the Airy disk [http://www.zbirding.info/zbirders/blogs/sing/archive/2006/08/09/189.aspx] in the direction perpendicular crest of the roof as this is a diffraction from the discontinuity at the roof crest.The unwanted interference effects are suppressed by vapour depositing a special dielectric coating known as a "phase-compensating coating" on the roof surfaces of the roof prism. This coating corrects for the difference in geometric phase between s- and p-polarized light so both have effectively the same phase shift and no interference degrades the image.

The multiple internal reflections also cause a polarization-dependent phase-lag of the transmitted light, in a manner similar to a Fresnel rhomb. This must be suppressed by multilayer "phase-correction coatings" applied to one of the roof surfaces to avoid unwanted interference effects and a loss of contrast in the image.In a roof prism without a phase correcting coating s-polarized and p-polarized light each acquire a different geometric phase as they pass through the upper prism. When the two polarized components are recombined interference between the s-polarized and p-polarized light results in an different intensity distribution perpendicular to the roof edge as compared to that along the roof edge. This effect reduces contrast and resolution in the image perpendicular to the roof edge. Giving an inferior image compared to that from a porro prism erecting system. This roof edge diffraction effect may also be seen as a diffraction spike perpendicular to the roof edge generated by bright points in the image.This effect can be seen in the elongation of the Airy disk [http://www.zbirding.info/zbirders/blogs/sing/archive/2006/08/09/189.aspx] in the direction perpendicular crest of the roof as this is a diffraction from the discontinuity at the roof crest.The unwanted interference effects are suppressed by vapour depositing a special dielectric coating known as a "phase-compensating coating" on the roof surfaces of the roof prism. This coating corrects for the difference in geometric phase between s- and p-polarized light so both have effectively the same phase shift and no interference degrades the image.

All of the entry and exit surfaces must be optically coated to minimize losses, though the type of coating has to be carefully chosen as the same faces of the prism act both as entry faces (desiring good anti-reflection coating) and internally reflective faces (require a coating maximizing reflection). A paper, "Progress in Binocular Design", by Konrad Siel at Swarovski shows that single-layer anti-reflective coatings on these surfaces maximized image contrast [http://www.optics.arizona.edu/optomech/references/papers/Seil%201991.pdf] . Reflection losses As the light is incident at a glass–air boundary with an angle less than the critical angle, total internal reflection does not occur at that surface. To mitigate this problem, a mirror coating is used on those sufaces. Typically an aluminum mirror coating reflectivity of 87% to 93%) or silver mirror coating (reflectivity of 95% to 98%) is used. The transmission of the prism can be improved by using a dielectric coating rather than a metallic mirror coating. This causes the prism surfaces to act as a dielectric mirror. The dielectric multilayer coating increases reflectivity from the prism surfaces by acting as a distributed Bragg reflector. A well-designed dielectric coating can provide a reflectivity of more than 99% across the visible light spectrum. This reflectivity is much improved compared to either an aluminum or silver mirror coating and the performance of the Schmidt-Pechan prism is similar to the Porro prism or the Abbe-Koenig prism.The requirement for a mirror coating makes the Schmidt-Pechan roof prism more lossy than the other image erectors using Porro prism or Abbe-Koenig prism that rely only on total internal reflections. Phase correction The multiple internal reflections also cause a polarization-dependent phase-lag of the transmitted light, in a manner similar to a Fresnel rhomb. This must be suppressed by multilayer "phase-correction coatings" applied to one of the roof surfaces to avoid unwanted interference effects and a loss of contrast in the image.In a roof prism without a phase correcting coating s-polarized and p-polarized light each acquire a different geometric phase as they pass through the upper prism. When the two polarized components are recombined interference between the s-polarized and p-polarized light results in an different intensity distribution perpendicular to the roof edge as compared to that along the roof edge. This effect reduces contrast and resolution in the image perpendicular to the roof edge. Giving an inferior image compared to that from a porro prism erecting system. This roof edge diffraction effect may also be seen as a diffraction spike perpendicular to the roof edge generated by bright points in the image.This effect can be seen in the elongation of the Airy disk [http://www.zbirding.info/zbirders/blogs/sing/archive/2006/08/09/189.aspx] in the direction perpendicular crest of the roof as this is a diffraction from the discontinuity at the roof crest.The unwanted interference effects are suppressed by vapour depositing a special dielectric coating known as a "phase-compensating coating" on the roof surfaces of the roof prism. This coating corrects for the difference in geometric phase between s- and p-polarized light so both have effectively the same phase shift and no interference degrades the image.

A simple setup would focus a point source of light onto a ground surface (a focusing screen) that is mounted on an optical rail (so you can move it along the optical axis). Once you have found the focal point, you move the surface a known distance away, and measure the size of the focal spot (I would recommend using an eyepiece graticule to make the measurement straightforward). Repeat this for a few different distances, and determine the slope of the straight line through the plot of spot radius vs distance to focal point. This slope represents the tangent of the half-angle of the iris subtended at the focal point.

Phase correction The multiple internal reflections also cause a polarization-dependent phase-lag of the transmitted light, in a manner similar to a Fresnel rhomb. This must be suppressed by multilayer "phase-correction coatings" applied to one of the roof surfaces to avoid unwanted interference effects and a loss of contrast in the image.In a roof prism without a phase correcting coating s-polarized and p-polarized light each acquire a different geometric phase as they pass through the upper prism. When the two polarized components are recombined interference between the s-polarized and p-polarized light results in an different intensity distribution perpendicular to the roof edge as compared to that along the roof edge. This effect reduces contrast and resolution in the image perpendicular to the roof edge. Giving an inferior image compared to that from a porro prism erecting system. This roof edge diffraction effect may also be seen as a diffraction spike perpendicular to the roof edge generated by bright points in the image.This effect can be seen in the elongation of the Airy disk [http://www.zbirding.info/zbirders/blogs/sing/archive/2006/08/09/189.aspx] in the direction perpendicular crest of the roof as this is a diffraction from the discontinuity at the roof crest.The unwanted interference effects are suppressed by vapour depositing a special dielectric coating known as a "phase-compensating coating" on the roof surfaces of the roof prism. This coating corrects for the difference in geometric phase between s- and p-polarized light so both have effectively the same phase shift and no interference degrades the image.

The Pechan prism is a composite of two prisms separated by an air gap. It will invert or revert (flip) the image depending up orientation of the prism but not both at the same time. By replacing the second prism in the Pechan design with a Schmidt prism the Schmidt-Pechan prism can both invert and revert the image and so act as an image rotator.The Schmidt-Pechan prism consists of two glass prisms separated by an air-gap. The second, Schmidt, prism both reverts and inverts the image but in doing so deviates the path by 45°. The first prism corrects for this delivering a beam at 45° into the Schmidt prism. The design of the first prism is such that the entrance beam and exit beam are coaxial i.e. the Schmidt-Pechan prism does not deviate the beam if centered on the optical axis.The lower prism uses one total internal reflection followed by a reflection from a mirrored surface to direct the beam into the second Schmidt prism so the orientation of the image is not changed.The upper prism inverts the image by three total internal reflections in the vertical plane through the roof ridge. The "roof" section of the Schmidt prism flips (reverts) the image laterally with two total internal reflections in the horizontal plane from the roof surface: once on each side of the roof. This latter pair of reflections can be considered as one reflection in the vertical plane. Both inversion and reversion together cause a 180° rotation of the image. The image's handedness is not changed. The reflection from the bottom surface of the first prism is not by total internal reflection since the light is incident at an angle less than the "critical angle". This is unlike other roof prisms like the Abbe-Koenig prism. This surface of the Schmidt-Pechan prism requires a reflective coating for this prism to be usable in practice. Problems with the Schmidt-Pechan prism Glass–air transitions All of the entry and exit surfaces must be optically coated to minimize losses, though the type of coating has to be carefully chosen as the same faces of the prism act both as entry faces (desiring good anti-reflection coating) and internally reflective faces (require a coating maximizing reflection). A paper, "Progress in Binocular Design", by Konrad Siel at Swarovski shows that single-layer anti-reflective coatings on these surfaces maximized image contrast [http://www.optics.arizona.edu/optomech/references/papers/Seil%201991.pdf] . Reflection losses As the light is incident at a glass–air boundary with an angle less than the critical angle, total internal reflection does not occur at that surface. To mitigate this problem, a mirror coating is used on those sufaces. Typically an aluminum mirror coating reflectivity of 87% to 93%) or silver mirror coating (reflectivity of 95% to 98%) is used. The transmission of the prism can be improved by using a dielectric coating rather than a metallic mirror coating. This causes the prism surfaces to act as a dielectric mirror. The dielectric multilayer coating increases reflectivity from the prism surfaces by acting as a distributed Bragg reflector. A well-designed dielectric coating can provide a reflectivity of more than 99% across the visible light spectrum. This reflectivity is much improved compared to either an aluminum or silver mirror coating and the performance of the Schmidt-Pechan prism is similar to the Porro prism or the Abbe-Koenig prism.The requirement for a mirror coating makes the Schmidt-Pechan roof prism more lossy than the other image erectors using Porro prism or Abbe-Koenig prism that rely only on total internal reflections. Phase correction The multiple internal reflections also cause a polarization-dependent phase-lag of the transmitted light, in a manner similar to a Fresnel rhomb. This must be suppressed by multilayer "phase-correction coatings" applied to one of the roof surfaces to avoid unwanted interference effects and a loss of contrast in the image.In a roof prism without a phase correcting coating s-polarized and p-polarized light each acquire a different geometric phase as they pass through the upper prism. When the two polarized components are recombined interference between the s-polarized and p-polarized light results in an different intensity distribution perpendicular to the roof edge as compared to that along the roof edge. This effect reduces contrast and resolution in the image perpendicular to the roof edge. Giving an inferior image compared to that from a porro prism erecting system. This roof edge diffraction effect may also be seen as a diffraction spike perpendicular to the roof edge generated by bright points in the image.This effect can be seen in the elongation of the Airy disk [http://www.zbirding.info/zbirders/blogs/sing/archive/2006/08/09/189.aspx] in the direction perpendicular crest of the roof as this is a diffraction from the discontinuity at the roof crest.The unwanted interference effects are suppressed by vapour depositing a special dielectric coating known as a "phase-compensating coating" on the roof surfaces of the roof prism. This coating corrects for the difference in geometric phase between s- and p-polarized light so both have effectively the same phase shift and no interference degrades the image.

The reflection from the bottom surface of the first prism is not by total internal reflection since the light is incident at an angle less than the "critical angle". This is unlike other roof prisms like the Abbe-Koenig prism. This surface of the Schmidt-Pechan prism requires a reflective coating for this prism to be usable in practice. Problems with the Schmidt-Pechan prism Glass–air transitions All of the entry and exit surfaces must be optically coated to minimize losses, though the type of coating has to be carefully chosen as the same faces of the prism act both as entry faces (desiring good anti-reflection coating) and internally reflective faces (require a coating maximizing reflection). A paper, "Progress in Binocular Design", by Konrad Siel at Swarovski shows that single-layer anti-reflective coatings on these surfaces maximized image contrast [http://www.optics.arizona.edu/optomech/references/papers/Seil%201991.pdf] . Reflection losses As the light is incident at a glass–air boundary with an angle less than the critical angle, total internal reflection does not occur at that surface. To mitigate this problem, a mirror coating is used on those sufaces. Typically an aluminum mirror coating reflectivity of 87% to 93%) or silver mirror coating (reflectivity of 95% to 98%) is used. The transmission of the prism can be improved by using a dielectric coating rather than a metallic mirror coating. This causes the prism surfaces to act as a dielectric mirror. The dielectric multilayer coating increases reflectivity from the prism surfaces by acting as a distributed Bragg reflector. A well-designed dielectric coating can provide a reflectivity of more than 99% across the visible light spectrum. This reflectivity is much improved compared to either an aluminum or silver mirror coating and the performance of the Schmidt-Pechan prism is similar to the Porro prism or the Abbe-Koenig prism.The requirement for a mirror coating makes the Schmidt-Pechan roof prism more lossy than the other image erectors using Porro prism or Abbe-Koenig prism that rely only on total internal reflections. Phase correction The multiple internal reflections also cause a polarization-dependent phase-lag of the transmitted light, in a manner similar to a Fresnel rhomb. This must be suppressed by multilayer "phase-correction coatings" applied to one of the roof surfaces to avoid unwanted interference effects and a loss of contrast in the image.In a roof prism without a phase correcting coating s-polarized and p-polarized light each acquire a different geometric phase as they pass through the upper prism. When the two polarized components are recombined interference between the s-polarized and p-polarized light results in an different intensity distribution perpendicular to the roof edge as compared to that along the roof edge. This effect reduces contrast and resolution in the image perpendicular to the roof edge. Giving an inferior image compared to that from a porro prism erecting system. This roof edge diffraction effect may also be seen as a diffraction spike perpendicular to the roof edge generated by bright points in the image.This effect can be seen in the elongation of the Airy disk [http://www.zbirding.info/zbirders/blogs/sing/archive/2006/08/09/189.aspx] in the direction perpendicular crest of the roof as this is a diffraction from the discontinuity at the roof crest.The unwanted interference effects are suppressed by vapour depositing a special dielectric coating known as a "phase-compensating coating" on the roof surfaces of the roof prism. This coating corrects for the difference in geometric phase between s- and p-polarized light so both have effectively the same phase shift and no interference degrades the image.

To mitigate this problem, a mirror coating is used on those sufaces. Typically an aluminum mirror coating reflectivity of 87% to 93%) or silver mirror coating (reflectivity of 95% to 98%) is used. The transmission of the prism can be improved by using a dielectric coating rather than a metallic mirror coating. This causes the prism surfaces to act as a dielectric mirror. The dielectric multilayer coating increases reflectivity from the prism surfaces by acting as a distributed Bragg reflector. A well-designed dielectric coating can provide a reflectivity of more than 99% across the visible light spectrum. This reflectivity is much improved compared to either an aluminum or silver mirror coating and the performance of the Schmidt-Pechan prism is similar to the Porro prism or the Abbe-Koenig prism.The requirement for a mirror coating makes the Schmidt-Pechan roof prism more lossy than the other image erectors using Porro prism or Abbe-Koenig prism that rely only on total internal reflections. Phase correction The multiple internal reflections also cause a polarization-dependent phase-lag of the transmitted light, in a manner similar to a Fresnel rhomb. This must be suppressed by multilayer "phase-correction coatings" applied to one of the roof surfaces to avoid unwanted interference effects and a loss of contrast in the image.In a roof prism without a phase correcting coating s-polarized and p-polarized light each acquire a different geometric phase as they pass through the upper prism. When the two polarized components are recombined interference between the s-polarized and p-polarized light results in an different intensity distribution perpendicular to the roof edge as compared to that along the roof edge. This effect reduces contrast and resolution in the image perpendicular to the roof edge. Giving an inferior image compared to that from a porro prism erecting system. This roof edge diffraction effect may also be seen as a diffraction spike perpendicular to the roof edge generated by bright points in the image.This effect can be seen in the elongation of the Airy disk [http://www.zbirding.info/zbirders/blogs/sing/archive/2006/08/09/189.aspx] in the direction perpendicular crest of the roof as this is a diffraction from the discontinuity at the roof crest.The unwanted interference effects are suppressed by vapour depositing a special dielectric coating known as a "phase-compensating coating" on the roof surfaces of the roof prism. This coating corrects for the difference in geometric phase between s- and p-polarized light so both have effectively the same phase shift and no interference degrades the image.

The Schmidt-Pechan prism consists of two glass prisms separated by an air-gap. The second, Schmidt, prism both reverts and inverts the image but in doing so deviates the path by 45°. The first prism corrects for this delivering a beam at 45° into the Schmidt prism. The design of the first prism is such that the entrance beam and exit beam are coaxial i.e. the Schmidt-Pechan prism does not deviate the beam if centered on the optical axis.The lower prism uses one total internal reflection followed by a reflection from a mirrored surface to direct the beam into the second Schmidt prism so the orientation of the image is not changed.The upper prism inverts the image by three total internal reflections in the vertical plane through the roof ridge. The "roof" section of the Schmidt prism flips (reverts) the image laterally with two total internal reflections in the horizontal plane from the roof surface: once on each side of the roof. This latter pair of reflections can be considered as one reflection in the vertical plane. Both inversion and reversion together cause a 180° rotation of the image. The image's handedness is not changed. The reflection from the bottom surface of the first prism is not by total internal reflection since the light is incident at an angle less than the "critical angle". This is unlike other roof prisms like the Abbe-Koenig prism. This surface of the Schmidt-Pechan prism requires a reflective coating for this prism to be usable in practice. Problems with the Schmidt-Pechan prism Glass–air transitions All of the entry and exit surfaces must be optically coated to minimize losses, though the type of coating has to be carefully chosen as the same faces of the prism act both as entry faces (desiring good anti-reflection coating) and internally reflective faces (require a coating maximizing reflection). A paper, "Progress in Binocular Design", by Konrad Siel at Swarovski shows that single-layer anti-reflective coatings on these surfaces maximized image contrast [http://www.optics.arizona.edu/optomech/references/papers/Seil%201991.pdf] . Reflection losses As the light is incident at a glass–air boundary with an angle less than the critical angle, total internal reflection does not occur at that surface. To mitigate this problem, a mirror coating is used on those sufaces. Typically an aluminum mirror coating reflectivity of 87% to 93%) or silver mirror coating (reflectivity of 95% to 98%) is used. The transmission of the prism can be improved by using a dielectric coating rather than a metallic mirror coating. This causes the prism surfaces to act as a dielectric mirror. The dielectric multilayer coating increases reflectivity from the prism surfaces by acting as a distributed Bragg reflector. A well-designed dielectric coating can provide a reflectivity of more than 99% across the visible light spectrum. This reflectivity is much improved compared to either an aluminum or silver mirror coating and the performance of the Schmidt-Pechan prism is similar to the Porro prism or the Abbe-Koenig prism.The requirement for a mirror coating makes the Schmidt-Pechan roof prism more lossy than the other image erectors using Porro prism or Abbe-Koenig prism that rely only on total internal reflections. Phase correction The multiple internal reflections also cause a polarization-dependent phase-lag of the transmitted light, in a manner similar to a Fresnel rhomb. This must be suppressed by multilayer "phase-correction coatings" applied to one of the roof surfaces to avoid unwanted interference effects and a loss of contrast in the image.In a roof prism without a phase correcting coating s-polarized and p-polarized light each acquire a different geometric phase as they pass through the upper prism. When the two polarized components are recombined interference between the s-polarized and p-polarized light results in an different intensity distribution perpendicular to the roof edge as compared to that along the roof edge. This effect reduces contrast and resolution in the image perpendicular to the roof edge. Giving an inferior image compared to that from a porro prism erecting system. This roof edge diffraction effect may also be seen as a diffraction spike perpendicular to the roof edge generated by bright points in the image.This effect can be seen in the elongation of the Airy disk [http://www.zbirding.info/zbirders/blogs/sing/archive/2006/08/09/189.aspx] in the direction perpendicular crest of the roof as this is a diffraction from the discontinuity at the roof crest.The unwanted interference effects are suppressed by vapour depositing a special dielectric coating known as a "phase-compensating coating" on the roof surfaces of the roof prism. This coating corrects for the difference in geometric phase between s- and p-polarized light so both have effectively the same phase shift and no interference degrades the image.