Aberration coefficient of distortion for a single surface, refractive or reflective, with the stop at the surface, is given by: with the peak aberration coefficient,

Hands-on Review ~ Kowa's new high-end spotting scope embodies the fluorite crystal objective lens and the fine engineeering that put Kowa Prominar scopes in the top tier of birding optics. With a 99mm objective lens, this is the biggest Kowa spotting scope. See how we like it compared to the 95mm Swarovski ATX scope. (2021)

You usually get a wider field of view with an 8-power binocular than you do with the same model in 10 power. A wider field of view makes it easier to spot a songbird among the branches (or a seabird on the waves. This is especially important in visually complex situations such as forest birding.

Aberration coefficient of distortion for a single surface, refractive or reflective, with the stop at the surface, is given by: with the peak aberration coefficient,

Hands-on Review ~ This is Zeiss's middle tier of the three lines of Zeiss binoculas. It costs less than half as much as the legendary Zeiss Victory SF binoculars. However, like the Victory SF line, it is hand made in Germany by a small team of skilled European technicians. It is a qualitative step up for many birders as they get more serious about birding.

Hands-on Review ~ The Zeiss Gavia scope bears comparison to the Vortex Razor HD, both of which became availble around 2017. Both have 85mm objective lenses. Both focus using a textured band around the middle of the scope. Both cost in the $1500-$2000 range. This article compares their design and quality.

Michael and Diane Porter are avid birdwatchers who have been reviewing binoculars and spotting scopes for over 20 years. They've surveyed hundreds of binoculars and scopes, testing them for optical qualities and noting the fit-and-feel characteristics of each instrument.

◄ 4.4. Defocus   ▐    4.6. Field curvature ►   4.5. IMAGE DISTORTION As a wavefront aberration, image distortion is caused by the change of magnification with the incident angle, with the actual wavefront being formed tilted with respect to a perfect (Gaussian) reference sphere. It is a consequence of the light cones for oblique angles coming in at a different angles, and using different portions of optical surface(s) than the near-axis cones. It changes the effective focal length for those converging cones, and with it their magnification, i.e. tilt angle. Some surfaces make focal length longer toward the edge, some shorter, and the final sum is the system distortion. In effect, the actual wavefront is tilted with respect to the Gaussian reference sphere, and the actual image point is shifted in the image space. The magnitude of shift increases with the third power of the incident angle, effectively inducing a varying point height magnification in the image space. The result is distortion of the image's geometric form but, since the wavefront remains spherical - or aberrated as determined by other factors - point-image quality itself is not affected. The aberration function of distortion is given by: Wt = Gρcosθ           (27)with G=gdα3 being the peak distortion aberration coefficient, g being the aberration coefficient (α is the field angle and d the aperture radius), and θ is the pupil angle. Since ray aberration caused by distortion is independent of pupil coordinates (ρ,θ) all rays meet at the image point, which is displaced radially in proportion to the cube of the point field angle α (FIG. 59). FIGURE 59: Illustration of the effect of image distortion: Gaussian image of a square centered in the field has its corner point C farther away from field center O than its mid-side point M by a factor of 21/2. Since distortion increases with the third power of off-center distance (strictly talking, field angle, but for small angles the difference between the rate of change of the two is negligible) in the image plane the corner point  C is shifted away from its perfect coordinates by a factor (21/2)3 more radially than the mid-side point M (this proportion remain constant, only the magnitude of deformation changes). In other words, the length of the aberrated extension CC' or CC" of the aberrated image of the square is larger than MM' or MM", respectively, by a factor of (OC/OM)3. As a result, the image is deformed, either inward (negative, or barrel distortion, blue), or outward (positive, or pincushion distortion, red). Since the amount of shift from the perfect coordinate is in proportion to the cube of off-axis angle, α3, linear distortion of any non-circular form centered in the field increases with the cube of its linear diameter; in effect, shape distortion increases with α2. Aberration coefficient of distortion for a single surface, refractive or reflective, with the stop at the surface, is given by: with the peak aberration coefficient, G = gα3D/2            (27.2)representing the peak wavefront error of tilt with respect to the reference sphere centered at Gaussian focus along the axis of aberration (n and n' are the refractive index of incident and refractive/reflective medium, respectively, and D is the aperture diameter). The aberration coefficient is zero for both, concave mirror (n=1, n'=-1) and a thin lens with the aperture stop at the surface. Distortion is introduced if the stop is displaced, which means that it is present in multi-element systems with the elements at more than insignificant separation. An exception is a sphere with the stop at its center of curvature, when it also has zero distortion, due to its unique symmetry. In general, distortion is negligible for small angular images, such are those of telescope objectives. However, it becomes significant at large angles, characteristic of the images viewed through telescope eyepieces. Picture below shows raytrace cross section of a 110-degree AFOV eyepiece, with about 50% positive (pincushion) distortion (entering cones are not near orthogonal to the Smyth lens because this particular eyepiece was designed for a binocular objective). The cones entering (actually exiting, since it is reverse raytracing) eyepiece on the right are different in their width, with the field edge cones being noticeably narrower. That is a consequence of their increased magnification (narrower cone forms larger Airy disc, i.e. image scale); in actual use, the entering cones would be of identical width, and the edge cone's exit pupil smaller, according to their increased magnification. Note that distortion in reverse raytracing has opposite sign to that in actual use.   ◄ 4.4. Defocus   ▐    4.6. Field curvature ►   Home  |  Comments

Distortion in opticsexamples

with G=gdα3 being the peak distortion aberration coefficient, g being the aberration coefficient (α is the field angle and d the aperture radius), and θ is the pupil angle. Since ray aberration caused by distortion is independent of pupil coordinates (ρ,θ) all rays meet at the image point, which is displaced radially in proportion to the cube of the point field angle α (FIG. 59). FIGURE 59: Illustration of the effect of image distortion: Gaussian image of a square centered in the field has its corner point C farther away from field center O than its mid-side point M by a factor of 21/2. Since distortion increases with the third power of off-center distance (strictly talking, field angle, but for small angles the difference between the rate of change of the two is negligible) in the image plane the corner point  C is shifted away from its perfect coordinates by a factor (21/2)3 more radially than the mid-side point M (this proportion remain constant, only the magnitude of deformation changes). In other words, the length of the aberrated extension CC' or CC" of the aberrated image of the square is larger than MM' or MM", respectively, by a factor of (OC/OM)3. As a result, the image is deformed, either inward (negative, or barrel distortion, blue), or outward (positive, or pincushion distortion, red). Since the amount of shift from the perfect coordinate is in proportion to the cube of off-axis angle, α3, linear distortion of any non-circular form centered in the field increases with the cube of its linear diameter; in effect, shape distortion increases with α2. Aberration coefficient of distortion for a single surface, refractive or reflective, with the stop at the surface, is given by: with the peak aberration coefficient,

Hands-on Review ~ In 2018, Kowa came out with a new 55mm Prominar travel scope. It is a remarkably small scope. It features the esteemed Kowa fluorite objective lens which has made the 88mm Kowa Prominar so popular. Here we compare the TSN-553 to four other travel scopes, including the economical Vortex Razor and the high-end Swarovski 65mm ATX.

Opticaldistortionmeaning

FIGURE 59: Illustration of the effect of image distortion: Gaussian image of a square centered in the field has its corner point C farther away from field center O than its mid-side point M by a factor of 21/2. Since distortion increases with the third power of off-center distance (strictly talking, field angle, but for small angles the difference between the rate of change of the two is negligible) in the image plane the corner point  C is shifted away from its perfect coordinates by a factor (21/2)3 more radially than the mid-side point M (this proportion remain constant, only the magnitude of deformation changes). In other words, the length of the aberrated extension CC' or CC" of the aberrated image of the square is larger than MM' or MM", respectively, by a factor of (OC/OM)3. As a result, the image is deformed, either inward (negative, or barrel distortion, blue), or outward (positive, or pincushion distortion, red). Since the amount of shift from the perfect coordinate is in proportion to the cube of off-axis angle, α3, linear distortion of any non-circular form centered in the field increases with the cube of its linear diameter; in effect, shape distortion increases with α2. Aberration coefficient of distortion for a single surface, refractive or reflective, with the stop at the surface, is given by: with the peak aberration coefficient,

Using Optics provides info on adjusting optics to fit yourself and caring for optics. Also basics of how binoculars and scopes work.

In general, distortion is negligible for small angular images, such are those of telescope objectives. However, it becomes significant at large angles, characteristic of the images viewed through telescope eyepieces. Picture below shows raytrace cross section of a 110-degree AFOV eyepiece, with about 50% positive (pincushion) distortion (entering cones are not near orthogonal to the Smyth lens because this particular eyepiece was designed for a binocular objective).

representing the peak wavefront error of tilt with respect to the reference sphere centered at Gaussian focus along the axis of aberration (n and n' are the refractive index of incident and refractive/reflective medium, respectively, and D is the aperture diameter). The aberration coefficient is zero for both, concave mirror (n=1, n'=-1) and a thin lens with the aperture stop at the surface. Distortion is introduced if the stop is displaced, which means that it is present in multi-element systems with the elements at more than insignificant separation. An exception is a sphere with the stop at its center of curvature, when it also has zero distortion, due to its unique symmetry. In general, distortion is negligible for small angular images, such are those of telescope objectives. However, it becomes significant at large angles, characteristic of the images viewed through telescope eyepieces. Picture below shows raytrace cross section of a 110-degree AFOV eyepiece, with about 50% positive (pincushion) distortion (entering cones are not near orthogonal to the Smyth lens because this particular eyepiece was designed for a binocular objective). The cones entering (actually exiting, since it is reverse raytracing) eyepiece on the right are different in their width, with the field edge cones being noticeably narrower. That is a consequence of their increased magnification (narrower cone forms larger Airy disc, i.e. image scale); in actual use, the entering cones would be of identical width, and the edge cone's exit pupil smaller, according to their increased magnification. Note that distortion in reverse raytracing has opposite sign to that in actual use.

Hands-on Review ~ A high-quality 32mm-sized binocular in the $1000 price range seems hard to find. The Zeiss Conquest HD is one. It is available in 10x32 and 8x32. Its nearest competitor would the slightly smaller Swarovski CL Companion in 8x30 and 10x30. We did a careful side-by-side comparison, and here is what we found.

Distortion in opticscalculator

Hands-on Review ~ When you look at the pinnacle of binocular optics (Leica, Swarovski, and Zeiss), it's hard to see a difference in the view of a bird in the treetop. Optically, all three are superb. The Leica Noctivid excels by its size and weight. REVIEW  |  SEE IN STORE

FIGURE 59: Illustration of the effect of image distortion: Gaussian image of a square centered in the field has its corner point C farther away from field center O than its mid-side point M by a factor of 21/2. Since distortion increases with the third power of off-center distance (strictly talking, field angle, but for small angles the difference between the rate of change of the two is negligible) in the image plane the corner point  C is shifted away from its perfect coordinates by a factor (21/2)3 more radially than the mid-side point M (this proportion remain constant, only the magnitude of deformation changes). In other words, the length of the aberrated extension CC' or CC" of the aberrated image of the square is larger than MM' or MM", respectively, by a factor of (OC/OM)3. As a result, the image is deformed, either inward (negative, or barrel distortion, blue), or outward (positive, or pincushion distortion, red). Since the amount of shift from the perfect coordinate is in proportion to the cube of off-axis angle, α3, linear distortion of any non-circular form centered in the field increases with the cube of its linear diameter; in effect, shape distortion increases with α2.

Hands-on Review ~ The new Swarovski BTX Ocular Module lets you see through a superb spotting scope while using both eyes! Your brain is designed to compare images coming from two eyes to construct what you see. Using two eyes makes the image more real, richer, and more natural. Here is a guided tour through this revolutionary optical product.

Hands-on Review ~ It's stunning from the moment you meet it. We've never seen a binocular with a shape quite like the NL Pure. It seems it was made to fit your hand. It has the widest field of view of any top binocular. REVIEW  |  SEE IN STORE

Hands-on Review ~ It seems that Zeiss has landed in a sweet spot with the new SFL binocular. High quality optics. The right size. Comfortable to carry and look through. We compare its pros and cons with other high-end binoculars.  REVIEW  |  SEE IN STORE

Distortion in opticsformula

The aberration coefficient is zero for both, concave mirror (n=1, n'=-1) and a thin lens with the aperture stop at the surface. Distortion is introduced if the stop is displaced, which means that it is present in multi-element systems with the elements at more than insignificant separation. An exception is a sphere with the stop at its center of curvature, when it also has zero distortion, due to its unique symmetry. In general, distortion is negligible for small angular images, such are those of telescope objectives. However, it becomes significant at large angles, characteristic of the images viewed through telescope eyepieces. Picture below shows raytrace cross section of a 110-degree AFOV eyepiece, with about 50% positive (pincushion) distortion (entering cones are not near orthogonal to the Smyth lens because this particular eyepiece was designed for a binocular objective). The cones entering (actually exiting, since it is reverse raytracing) eyepiece on the right are different in their width, with the field edge cones being noticeably narrower. That is a consequence of their increased magnification (narrower cone forms larger Airy disc, i.e. image scale); in actual use, the entering cones would be of identical width, and the edge cone's exit pupil smaller, according to their increased magnification. Note that distortion in reverse raytracing has opposite sign to that in actual use.

Getting to see the big picture ... People who wear glasses can get cheated out of part of the image. A binocular should let you see the whole image. Yet some binoculars make lose the outer part of the image for a person wearing glasses. Here's how to tell if a particular binocular will work with your glasses.

Imagedistortion inradiography

The main focus knob adjusts both the left and the right sides of the binocular at the same time. However, your two eyes may not focus at exactly the same distance, so you would be left with one eye slightly out of focus. In case yours eyes have such a difference, the diopter adjustment lets you change the focus of just the right side. Here's how to set it.

Hands-on Review ~ We review mid-sized binoculars that you'll always want to take along... because they're bright and clear but smallish and light in weight. Read this report on which are the best buys among 13 mid-sized binoculars, ranging from top of the field to the super-economical. (2019)

Wonder how binoculars work? Here's an easy demonstration you can do. All you need are two ordinary magnifying glasses and a piece of tracing paper.

We have hands-on experience with these optics, and we'd like to help you find just the right equipment for your own eyes and hands. (Whether you buy from us or not!)

Barreldistortion

Here is why a 32mm binocular is smaller, lighter weight, and less expensive than a 42mm. And why for most people of an (ahem) mature age, it is just as bright as a binocular with larger objective lenses. As a bonus, an strange as it may seem, the 32mm binocular usually has a wider field of view than the 42mm of the same magnification.

Hands-on Review ~ It knocked her socks off when Diane first looked through a Zeiss Victory SF binocular in 2015. How it felt in her hands! How it fit against her eyes! She only wished it came in 32mm. Now it does. Here is Diane's report. (2020) REVIEW  |  SEE IN STORE

Michael and Diane Porter 800-779-7256 Email: dporter@lisco.com Birdwatching Dot Com Online Store 2197 236th Blvd. Fairfield, IA 52556

Hands-on Review ~  They're the most comfortable binoculars I've ever held. They're really light. The barrels narrow in just the right place. They're not round in the center. They're designed for the way human hands are positioned when holding binoculars, with the narrowing on the diagonal. REVIEW  |  SEE IN STORE

This article discusses why most birders choose angled scopes rather than straight models. How it affects the steadiness of the image. Why it's easier to share the view. How it helps you look up or down.

Hands-on Review ~ Before Swarovski came out with their ATX/STX oculars scope system, the usual approach was to make a small eyepiece and a long body. Swarovski's completely new approach is a modular design divides the scope in a new and unique manner. With many advantages. This article reviews looks at the construction and performance improvements of Swarovski's design.

More binoculars are ruined by bad cleaning technique than by being dropped. You've seen someone do it. Breathe on the binocular's eyepiece and then rub the glass with the corner of a shirt. Poor birder, he never knew he just degraded every image he would ever see with that binocular again. Here's the right way to clean your binoculars.

Hands-on Review ~ New in 2019, Vortex's Diamondback looks like the olderr version. But they say "HD," indicating higher quality optical glass. We compared the new and old HD 8x42 Diamondbacks side by side. REVIEW  |  SEE HDs IN STORE

The cones entering (actually exiting, since it is reverse raytracing) eyepiece on the right are different in their width, with the field edge cones being noticeably narrower. That is a consequence of their increased magnification (narrower cone forms larger Airy disc, i.e. image scale); in actual use, the entering cones would be of identical width, and the edge cone's exit pupil smaller, according to their increased magnification. Note that distortion in reverse raytracing has opposite sign to that in actual use.

Hands-on Review ~  The new 52mm NL Pure binoculars are a giant step in stunning optics by Swarovski. We tested them personally and found them amazingly bright and incredibly clear.  The laws of optics say a larger diameter lens has more resolution and detail in its image. REVIEW  |  SEE IN STORE

If your binoculars are not fun to look through, if they give you a feeling of strain or a headache, they may be out of alignment. Here's a simple way that you can test if your binoculars are grossly out of alignment.

Wt = Gρcosθ           (27)with G=gdα3 being the peak distortion aberration coefficient, g being the aberration coefficient (α is the field angle and d the aperture radius), and θ is the pupil angle. Since ray aberration caused by distortion is independent of pupil coordinates (ρ,θ) all rays meet at the image point, which is displaced radially in proportion to the cube of the point field angle α (FIG. 59). FIGURE 59: Illustration of the effect of image distortion: Gaussian image of a square centered in the field has its corner point C farther away from field center O than its mid-side point M by a factor of 21/2. Since distortion increases with the third power of off-center distance (strictly talking, field angle, but for small angles the difference between the rate of change of the two is negligible) in the image plane the corner point  C is shifted away from its perfect coordinates by a factor (21/2)3 more radially than the mid-side point M (this proportion remain constant, only the magnitude of deformation changes). In other words, the length of the aberrated extension CC' or CC" of the aberrated image of the square is larger than MM' or MM", respectively, by a factor of (OC/OM)3. As a result, the image is deformed, either inward (negative, or barrel distortion, blue), or outward (positive, or pincushion distortion, red). Since the amount of shift from the perfect coordinate is in proportion to the cube of off-axis angle, α3, linear distortion of any non-circular form centered in the field increases with the cube of its linear diameter; in effect, shape distortion increases with α2. Aberration coefficient of distortion for a single surface, refractive or reflective, with the stop at the surface, is given by: with the peak aberration coefficient, G = gα3D/2            (27.2)representing the peak wavefront error of tilt with respect to the reference sphere centered at Gaussian focus along the axis of aberration (n and n' are the refractive index of incident and refractive/reflective medium, respectively, and D is the aperture diameter). The aberration coefficient is zero for both, concave mirror (n=1, n'=-1) and a thin lens with the aperture stop at the surface. Distortion is introduced if the stop is displaced, which means that it is present in multi-element systems with the elements at more than insignificant separation. An exception is a sphere with the stop at its center of curvature, when it also has zero distortion, due to its unique symmetry. In general, distortion is negligible for small angular images, such are those of telescope objectives. However, it becomes significant at large angles, characteristic of the images viewed through telescope eyepieces. Picture below shows raytrace cross section of a 110-degree AFOV eyepiece, with about 50% positive (pincushion) distortion (entering cones are not near orthogonal to the Smyth lens because this particular eyepiece was designed for a binocular objective). The cones entering (actually exiting, since it is reverse raytracing) eyepiece on the right are different in their width, with the field edge cones being noticeably narrower. That is a consequence of their increased magnification (narrower cone forms larger Airy disc, i.e. image scale); in actual use, the entering cones would be of identical width, and the edge cone's exit pupil smaller, according to their increased magnification. Note that distortion in reverse raytracing has opposite sign to that in actual use.   ◄ 4.4. Defocus   ▐    4.6. Field curvature ►   Home  |  Comments

In many of these surveys, a team of Iowa birders participated by trying out the optics and contributing their impressions and opinions.

As a wavefront aberration, image distortion is caused by the change of magnification with the incident angle, with the actual wavefront being formed tilted with respect to a perfect (Gaussian) reference sphere. It is a consequence of the light cones for oblique angles coming in at a different angles, and using different portions of optical surface(s) than the near-axis cones. It changes the effective focal length for those converging cones, and with it their magnification, i.e. tilt angle. Some surfaces make focal length longer toward the edge, some shorter, and the final sum is the system distortion. In effect, the actual wavefront is tilted with respect to the Gaussian reference sphere, and the actual image point is shifted in the image space. The magnitude of shift increases with the third power of the incident angle, effectively inducing a varying point height magnification in the image space. The result is distortion of the image's geometric form but, since the wavefront remains spherical - or aberrated as determined by other factors - point-image quality itself is not affected. The aberration function of distortion is given by: Wt = Gρcosθ           (27)with G=gdα3 being the peak distortion aberration coefficient, g being the aberration coefficient (α is the field angle and d the aperture radius), and θ is the pupil angle. Since ray aberration caused by distortion is independent of pupil coordinates (ρ,θ) all rays meet at the image point, which is displaced radially in proportion to the cube of the point field angle α (FIG. 59). FIGURE 59: Illustration of the effect of image distortion: Gaussian image of a square centered in the field has its corner point C farther away from field center O than its mid-side point M by a factor of 21/2. Since distortion increases with the third power of off-center distance (strictly talking, field angle, but for small angles the difference between the rate of change of the two is negligible) in the image plane the corner point  C is shifted away from its perfect coordinates by a factor (21/2)3 more radially than the mid-side point M (this proportion remain constant, only the magnitude of deformation changes). In other words, the length of the aberrated extension CC' or CC" of the aberrated image of the square is larger than MM' or MM", respectively, by a factor of (OC/OM)3. As a result, the image is deformed, either inward (negative, or barrel distortion, blue), or outward (positive, or pincushion distortion, red). Since the amount of shift from the perfect coordinate is in proportion to the cube of off-axis angle, α3, linear distortion of any non-circular form centered in the field increases with the cube of its linear diameter; in effect, shape distortion increases with α2. Aberration coefficient of distortion for a single surface, refractive or reflective, with the stop at the surface, is given by: with the peak aberration coefficient, G = gα3D/2            (27.2)representing the peak wavefront error of tilt with respect to the reference sphere centered at Gaussian focus along the axis of aberration (n and n' are the refractive index of incident and refractive/reflective medium, respectively, and D is the aperture diameter). The aberration coefficient is zero for both, concave mirror (n=1, n'=-1) and a thin lens with the aperture stop at the surface. Distortion is introduced if the stop is displaced, which means that it is present in multi-element systems with the elements at more than insignificant separation. An exception is a sphere with the stop at its center of curvature, when it also has zero distortion, due to its unique symmetry. In general, distortion is negligible for small angular images, such are those of telescope objectives. However, it becomes significant at large angles, characteristic of the images viewed through telescope eyepieces. Picture below shows raytrace cross section of a 110-degree AFOV eyepiece, with about 50% positive (pincushion) distortion (entering cones are not near orthogonal to the Smyth lens because this particular eyepiece was designed for a binocular objective). The cones entering (actually exiting, since it is reverse raytracing) eyepiece on the right are different in their width, with the field edge cones being noticeably narrower. That is a consequence of their increased magnification (narrower cone forms larger Airy disc, i.e. image scale); in actual use, the entering cones would be of identical width, and the edge cone's exit pupil smaller, according to their increased magnification. Note that distortion in reverse raytracing has opposite sign to that in actual use.   ◄ 4.4. Defocus   ▐    4.6. Field curvature ►   Home  |  Comments

The newest thing ~ The AX Visio is a binocular — a superb, world-class binocular — but it's so much more. It identifies the bird you're looking at, using integrated Merlin Bird ID intelligence. It has a built-in camera that takes a picture ofas you're looking at the bird. It lets you share by guiding your friend exactly to where you're looking. And by the way, it's also a compass.

Pincushiondistortion

Pincushiondistortion in optics

In the movies, somebody picks up binoculars and sees a sort of dumbell shape. Oh, so wrong! You want to see one image. Like you do in real life. Here is how to set your binoculars to get the right view.

Hands-on Review ~ Swarovski has extended their legendary optics with a tiny new pocket binocular, the Curio 7x21. It's even smaller than the traditional 8x25 and 10x25 Swarovski pockets. REVIEW  |  SEE IN STORE

Hands-on Review ~ It's a new choice in a pocket scope with top optical quality. At 34.2 ounces and 10.2 inches long, the new Swarovski ATC scope is a smaller version of the esteemed ATX scope line. Rest your elbows on a table and you can get by without a tripod at all. It fits in a photo-vest’s cargo pocket. (2022)

Hands-on Review ~  Recently I got my hands on the new Zeiss 8x30 SFL binocular. And now, when I reach for binoculars for a little casual birding, often it’s the 8x30 SFL that goes with me. It seems to know how to stay out of the way but be there when I need it. REVIEW  |  SEE IN STORE