Waveplates are constructed out of a birefringent material (such as quartz or mica, or even plastic), for which the index of refraction is different for light linearly polarized along one or the other of two certain perpendicular crystal axes. The behavior of a waveplate (that is, whether it is a half-wave plate, a quarter-wave plate, etc.) depends on the thickness of the crystal, the wavelength of light, and the variation of the index of refraction. By appropriate choice of the relationship between these parameters, it is possible to introduce a controlled phase shift between the two polarization components of a light wave, thereby altering its polarization.[1] With an engineered combination of two birefringent materials, an achromatic waveplate[2] can be manufactured such that the spectral response of its phase retardance can be nearly flat.

Since the divergent rays now travel different distances, some move out of phase and begin to interfere with each other — adding in some places and partially or completely canceling out in others. This interference produces a diffraction pattern with peak intensities where the amplitude of the light waves add, and less light where they subtract. If one were to measure the intensity of light reaching each position on a line, the measurements would appear as bands similar to those shown below.

If the axis of polarization of the incident wave is chosen so that it makes a 45° with the fast and slow axes of the waveplate, then Ef = Es ≡ E, and the resulting wave upon exiting the waveplate is

For an ideal circular aperture, the 2-D diffraction pattern is called an "airy disk," after its discoverer George Airy. The width of the airy disk is used to define the theoretical maximum resolution for an optical system (defined as the diameter of the first dark circle).

In practice, the diffraction limit doesn't necessarily bring about an abrupt change; there is actually a gradual transition between when diffraction is and is not visible. Furthermore, this limit is only a best-case scenario when using an otherwise perfect lens; real-world results may vary.

Science · Contrast (vision), the contradiction in form, colour and light between parts of an image · Contrast (statistics), a combination of averages whose ...

Another complication is that sensors utilizing a Bayer array allocate twice the fraction of pixels to green as red or blue light, and then interpolate these colors to produce the final full color image. This means that as the diffraction limit is approached, the first signs will be a loss of resolution in green and pixel-level luminosity. Blue light requires the smallest apertures (highest f-stop) in order to reduce its resolution due to diffraction.

For a single waveplate changing the wavelength of the light introduces a linear error in the phase. Tilt of the waveplate enters via a factor of 1/cos θ (where θ is the angle of tilt) into the path length and thus only quadratically into the phase. For the extraordinary polarization the tilt also changes the refractive index to the ordinary via a factor of cos θ, so combined with the path length, the phase shift for the extraordinary light due to tilt is zero.

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Camera Canon EOS 1Ds Canon EOS 1Ds Mk II Canon EOS 1Ds Mk III, 5D Mk II Canon EOS 1D Canon EOS 1D Mk II Canon EOS 1D Mk III Canon EOS 1D Mk IV Canon EOS 1D X Canon EOS 5D Canon EOS 5D Mk III Canon EOS 7D,60D,550D,600D,650D,1D C Canon EOS 50D, 500D Canon EOS 40D, 400D, 1000D Canon EOS 30D, 20D, 350D Canon EOS 1100D Canon PowerShot G1 X Canon PowerShot G11, G12, S95 Canon PowerShot G9, S100 Canon PowerShot G6 Nikon D3, D3S / D700 Nikon D40, D50, D70 Nikon D4 Nikon D60, D80, D3000 Nikon D3X Nikon D2X, D90, D300, D5000 Nikon D800 Nikon D5100, D7000 Sony SLT-A65, SLT-A77, NEX-7 Sony DSC-RX100

As a result of the sensor's anti-aliasing filter (and the Rayleigh criterion above), an airy disk can have a diameter of about 2-3 pixels before diffraction limits resolution (assuming an otherwise perfect lens). However, diffraction will likely have a visual impact prior to reaching this diameter.

In Raman spectroscopy, the information of inelestically scattered monochromatic (laser) light is used to investigate the chemical nature of matter. This process ...

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Stacking a series of different-order waveplates with polarization filters between them yields a Lyot filter. Either the filters can be rotated, or the waveplates can be replaced with liquid crystal layers, to obtain a widely tunable pass band in optical transmission spectrum.

diffraction翻译

This calculator shows a camera as being diffraction limited when the diameter of the airy disk exceeds what is typically resolvable in an 8x10 inch print viewed from one foot. Click "show advanced" to change the criteria for reaching this limit. The "set circle of confusion based on pixels" checkbox indicates when diffraction is likely to become visible on a computer at 100% scale. For a further explanation of each input setting, also see the depth of field calculator.

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The form below calculates the size of the airy disk and assesses whether the camera has become diffraction limited. Click on "show advanced" to define a custom circle of confusion (CoC), or to see the influence of pixel size.

Electron diffraction

The polarization of the incoming photon (or beam) can be resolved as two polarizations on the x and y axis. If the input polarization is parallel to the fast or slow axis, then there is no polarization of the other axis, so the output polarization is the same as the input (only the phase more or less delayed). If the input polarization is 45° to the fast and slow axis, the polarization on those axes are equal. But the phase of the output of the slow axis will be delayed 90° with the output of the fast axis. If not the amplitude but both sine values are displayed, then x and y combined will describe a circle. With other angles than 0° or 45° the values in fast and slow axis will differ and their resultant output will describe an ellipse.

The sensitive-tint (full-wave) and quarter-wave plates are widely used in the field of optical mineralogy. Addition of plates between the polarizers of a petrographic microscope makes easier the optical identification of minerals in thin sections of rocks,[3] in particular by allowing deduction of the shape and orientation of the optical indicatrices within the visible crystal sections.

Diffraction thus sets a fundamental resolution limit that is independent of the number of megapixels, or the size of the film format. It depends only on the f-number of your lens, and on the wavelength of light being imaged. One can think of it as the smallest theoretical "pixel" of detail in photography. Furthermore, the onset of diffraction is gradual; prior to limiting resolution, it can still reduce small-scale contrast by causing airy disks to partially overlap.

Diffraction is an optical effect which limits the total resolution of your photography — no matter how many megapixels your camera may have. It happens because light begins to disperse or "diffract" when passing through a small opening (such as your camera's aperture). This effect is normally negligible, since smaller apertures often improve sharpness by minimizing lens aberrations. However, for sufficiently small apertures, this strategy becomes counterproductive — at which point your camera is said to have become diffraction limited. Knowing this limit can help maximize detail, and avoid an unnecessarily long exposure or high ISO speed.

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For additional reading on this topic, also see the addendum: Digital Camera Diffraction, Part 2: Resolution, Color & Micro-Contrast

For a quarter-wave plate, the relationship between L, Δn, and λ0 is chosen so that the phase shift between polarization components is Γ = π/2. Now suppose a linearly polarized wave is incident on the crystal. This wave can be written as

Some diffraction is often ok if you are willing to sacrifice sharpness at the focal plane in exchange for sharpness outside the depth of field. Alternatively, very small apertures may be required to achieve sufficiently long exposures, such as to induce motion blur with flowing water. In other words, diffraction is just something to be aware of when choosing your exposure settings, similar to how one would balance other trade-offs such as noise (ISO) vs shutter speed.

Since the size of the airy disk also depends on the wavelength of light, each of the three primary colors will reach its diffraction limit at a different aperture. The calculation above assumes light in the middle of the visible spectrum (~550 nm). Typical digital SLR cameras can capture light with a wavelength of anywhere from 450 to 680 nm, so at best the airy disk would have a diameter of 80% the size shown above (for pure blue light).

A waveplate works by shifting the phase between two perpendicular polarization components of the light wave. A typical waveplate is simply a birefringent crystal with a carefully chosen orientation and thickness. The crystal is cut into a plate, with the orientation of the cut chosen so that the optic axis of the crystal is parallel to the surfaces of the plate. This results in two axes in the plane of the cut: the ordinary axis, with index of refraction no, and the extraordinary axis, with index of refraction ne. The ordinary axis is perpendicular to the optic axis. The extraordinary axis is parallel to the optic axis. For a light wave normally incident upon the plate, the polarization component along the ordinary axis travels through the crystal with a speed vo = c/no, while the polarization component along the extraordinary axis travels with a speed ve = c/ne. This leads to a phase difference between the two components as they exit the crystal. When ne < no, as in calcite, the extraordinary axis is called the fast axis and the ordinary axis is called the slow axis. For ne > no the situation is reversed.

By surfacing the prescription on the inside curve of the lens as opposed to the outside as is the case in non-digital lens product, the gain in proximity to our ...

Reflection, refraction diffraction

Although the above diagrams help give a feel for the concept of diffraction, only real-world photography can show its visual impact. The following series of images were taken on the Canon EOS 20D, which typically exhibits softening from diffraction beyond about f/11. Move your mouse over each f-number to see how these impact fine detail:

Shapes and Types. Lenses come in a variety of shapes including biconvex, biconcave, plano-convex, plano-concave, positive meniscus and negative meniscus.

For a half-wave plate, the relationship between L, Δn, and λ0 is chosen so that the phase shift between polarization components is Γ = π. Now suppose a linearly polarized wave with polarization vector p ^ {\displaystyle \mathbf {\hat {p}} } is incident on the crystal. Let θ denote the angle between p ^ {\displaystyle \mathbf {\hat {p}} } and f ^ {\displaystyle \mathbf {\hat {f}} } , where f ^ {\displaystyle \mathbf {\hat {f}} } is the vector along the waveplate's fast axis. Let z denote the propagation axis of the wave. The electric field of the incident wave is E e i ( k z − ω t ) = E p ^ e i ( k z − ω t ) = E ( cos ⁡ θ f ^ + sin ⁡ θ s ^ ) e i ( k z − ω t ) , {\displaystyle \mathbf {E} \,\mathrm {e} ^{i(kz-\omega t)}=E\,\mathbf {\hat {p}} \,\mathrm {e} ^{i(kz-\omega t)}=E(\cos \theta \,\mathbf {\hat {f}} +\sin \theta \,\mathbf {\hat {s}} )\mathrm {e} ^{i(kz-\omega t)},} where s ^ {\displaystyle \mathbf {\hat {s}} } lies along the waveplate's slow axis. The effect of the half-wave plate is to introduce a phase shift term eiΓ = eiπ = −1 between the f and s components of the wave, so that upon exiting the crystal the wave is now given by E ( cos ⁡ θ f ^ − sin ⁡ θ s ^ ) e i ( k z − ω t ) = E [ cos ⁡ ( − θ ) f ^ + sin ⁡ ( − θ ) s ^ ] e i ( k z − ω t ) . {\displaystyle E(\cos \theta \,\mathbf {\hat {f}} -\sin \theta \,\mathbf {\hat {s}} )\mathrm {e} ^{i(kz-\omega t)}=E[\cos(-\theta )\mathbf {\hat {f}} +\sin(-\theta )\mathbf {\hat {s}} ]\mathrm {e} ^{i(kz-\omega t)}.} If p ^ ′ {\displaystyle \mathbf {\hat {p}} '} denotes the polarization vector of the wave exiting the waveplate, then this expression shows that the angle between p ^ ′ {\displaystyle \mathbf {\hat {p}} '} and f ^ {\displaystyle \mathbf {\hat {f}} } is −θ. Evidently, the effect of the half-wave plate is to mirror the wave's polarization vector through the plane formed by the vectors f ^ {\displaystyle \mathbf {\hat {f}} } and z ^ {\displaystyle \mathbf {\hat {z}} } . For linearly polarized light, this is equivalent to saying that the effect of the half-wave plate is to rotate the polarization vector through an angle 2θ; however, for elliptically polarized light the half-wave plate also has the effect of inverting the light's handedness.[1]

A full-wave plate introduces a phase difference of exactly one wavelength between the two polarization directions, for one wavelength of light. In optical mineralogy, it is common to use a full-wave plate designed for green light (a wavelength near 540 nm). Linearly polarized white light which passes through the plate becomes elliptically polarized, except for that green light wavelength, which will remain linear. If a linear polarizer oriented perpendicular to the original polarization is added, this green wavelength is fully extinguished but elements of the other colors remain. This means that under these conditions the plate will appear an intense shade of red-violet, sometimes known as "sensitive tint".[4] This gives rise to this plate's alternative names, the sensitive-tint plate or (less commonly) red-tint plate. These plates are widely used in mineralogy to aid in identification of minerals in thin sections of rocks.[3]

If the axis of polarization of the incident wave is chosen so that it makes a 0° with the fast or slow axes of the waveplate, then the polarization will not change, so remains linear. If the angle is in between 0° and 45° the resulting wave has an elliptical polarization.

Even when a camera system is near or just past its diffraction limit, other factors such as focus accuracy, motion blur and imperfect lenses are likely to be more significant. Diffraction therefore limits total sharpness only when using a sturdy tripod, mirror lock-up and a very high quality lens.

Technical Note: Independence of Focal Length Since the physical size of an aperture is larger for telephoto lenses (f/4 has a 50 mm diameter at 200 mm, but only a 25 mm diameter at 100 mm), why doesn't the airy disk become smaller? This is because longer focal lengths also cause light to travel farther before hitting the camera sensor -- thus increasing the distance over which the airy disk can continue to diverge. The competing effects of larger aperture and longer focal length therefore cancel, leaving only the f-number as being important (which describes focal length relative to aperture size).

Note: above airy disk will appear narrower than its specified diameter (since this is defined by where it reaches its first minimum instead of by the visible inner bright region).

Although the birefringence Δn may vary slightly due to dispersion, this is negligible compared to the variation in phase difference according to the wavelength of the light due to the fixed path difference (λ0 in the denominator in the above equation). Waveplates are thus manufactured to work for a particular range of wavelengths. The phase variation can be minimized by stacking two waveplates that differ by a tiny amount in thickness back-to-back, with the slow axis of one along the fast axis of the other. With this configuration, the relative phase imparted can be, for the case of a quarter-wave plate, one-fourth a wavelength rather than three-fourths or one-fourth plus an integer. This is called a zero-order waveplate.

A circulating polarization can be visualized as the sum of two linear polarizations with a phase difference of 90°. The output depends on the polarization of the input. Suppose polarization axes x and y parallel with the slow and fast axis of the waveplate:

This should not lead you to think that "larger apertures are better," even though very small apertures create a soft image; most lenses are also quite soft when used wide open (at the largest aperture available). Camera systems typically have an optimal aperture in between the largest and smallest settings; with most lenses, optimal sharpness is often close to the diffraction limit, but with some lenses this may even occur prior to the diffraction limit. These calculations only show when diffraction becomes significant, not necessarily the location of optimum sharpness (see camera lens quality: MTF, resolution & contrast for more on this).

In practical terms, the plate is inserted between the perpendicular polarizers at an angle of 45 degrees. This allows two different procedures to be carried out to investigate the mineral under the crosshairs of the microscope. Firstly, in ordinary cross polarized light, the plate can be used to distinguish the orientation of the optical indicatrix relative to crystal elongation – that is, whether the mineral is "length slow" or "length fast" – based on whether the visible interference colors increase or decrease by one order when the plate is added. Secondly, a slightly more complex procedure allows for a tint plate to be used in conjunction with interference figure techniques to allow measurement of the optic angle of the mineral. The optic angle (often notated as "2V") can both be diagnostic of mineral type, as well as in some cases revealing information about the variation of chemical composition within a single mineral type.

Diffraction pattern

Note: CF = "crop factor" (commonly referred to as the focal length multiplier); assumes square pixels, 4:3 aspect ratio for compact digital and 3:2 for SLR. *Calculator assumes that your camera sensor uses the typical bayer array.

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Diffraction

Depending on the thickness of the crystal, light with polarization components along both axes will emerge in a different polarization state. The waveplate is characterized by the amount of relative phase, Γ, that it imparts on the two components, which is related to the birefringence Δn and the thickness L of the crystal by the formula

Waveplates in general, as well as polarizers, can be described using the Jones matrix formalism, which uses a vector to represent the polarization state of light and a matrix to represent the linear transformation of a waveplate or polarizer.

Airy Diameter: 21.3 µm Camera Canon EOS 1Ds Canon EOS 1Ds Mk II Canon EOS 1Ds Mk III, 5D Mk II Canon EOS 1D Canon EOS 1D Mk II Canon EOS 1D Mk III Canon EOS 1D Mk IV Canon EOS 1D X Canon EOS 5D Canon EOS 5D Mk III Canon EOS 7D,60D,550D,600D,650D,1D C Canon EOS 50D, 500D Canon EOS 40D, 400D, 1000D Canon EOS 30D, 20D, 350D Canon EOS 1100D Canon PowerShot G1 X Canon PowerShot G11, G12, S95 Canon PowerShot G9, S100 Canon PowerShot G6 Nikon D3, D3S / D700 Nikon D40, D50, D70 Nikon D4 Nikon D60, D80, D3000 Nikon D3X Nikon D2X, D90, D300, D5000 Nikon D800 Nikon D5100, D7000 Sony SLT-A65, SLT-A77, NEX-7 Sony DSC-RX100 Pixel Diameter: 6.9 µm

A multiple-order waveplate is made from a single birefringent crystal that produces an integer multiple of the rated retardance (for example, a multiple-order half-wave plate may have an absolute retardance of 37λ/2). By contrast, a zero-order waveplate produces exactly the specified retardance. This can be accomplished by combining two multiple-order wave plates such that the difference in their retardances yields the net (true) retardance of the waveplate. Zero-order waveplates are less sensitive to temperature and wavelength shifts, but are more expensive than multiple-order ones.[5]

The size of the airy disk is primarily useful in the context of pixel size. The following interactive tool shows a single airy disk compared to pixel size for several camera models:

The magnification of the ocular lenses on your scope is 10X. Objective lens X Ocular lens = Total magnification. For example: low power: (10X)(10X) = ...

Single slit diffraction

Are smaller pixels somehow worse? Not necessarily. Just because the diffraction limit has been reached (with large pixels) does not necessarily mean an image is any worse than if smaller pixels had been used (and the limit was surpassed); both scenarios still have the same total resolution (even though the smaller pixels produce a larger file). However, the camera with the smaller pixels will render the photo with fewer artifacts (such as color moiré and aliasing). Smaller pixels also give more creative flexibility, since these can yield a higher resolution if using a larger aperture is possible (such as when the depth of field can be shallow). On the other hand, when other factors such as noise and dynamic range are considered, the "small vs. large" pixels debate becomes more complicated...

A polarization-independent phase shift of zero order needs a plate with thickness of one wavelength. For calcite the refractive index changes in the first decimal place, so that a true zero order plate is ten times as thick as one wavelength. For quartz and magnesium fluoride the refractive index changes in the second decimal place and true zero order plates are common for wavelengths above 1 μm.

A common use of waveplates—particularly the sensitive-tint (full-wave) and quarter-wave plates—is in optical mineralogy. Addition of plates between the polarizers of a petrographic microscope makes the optical identification of minerals in thin sections of rocks easier,[3] in particular by allowing deduction of the shape and orientation of the optical indicatrices within the visible crystal sections. This alignment can allow discrimination between minerals which otherwise appear very similar in plane polarized and cross polarized light.

Note how most of the lines in the fabric are still resolved at f/11, but have slightly lower small-scale contrast or acutance (particularly where the fabric lines are very close). This is because the airy disks are only partially overlapping, similar to the effect on adjacent rows of alternating black and white airy disks (as shown on the right). By f/22, almost all fine lines have been smoothed out because the airy disks are larger than this detail.

Fresnel diffraction

As two examples, the Canon EOS 20D begins to show diffraction at around f/11, whereas the Canon PowerShot G6 begins to show its effects at only about f/5.6. On the other hand, the Canon G6 does not require apertures as small as the 20D in order to achieve the same depth of field (due to its much smaller sensor size).

A waveplate or retarder is an optical device that alters the polarization state of a light wave travelling through it. Two common types of waveplates are the half-wave plate, which rotates the polarization direction of linearly polarized light, and the quarter-wave plate, which converts between different elliptical polarizations (such as the special case of converting from linearly polarized light to circularly polarized light and vice versa.)[1]

where the f and s axes are the quarter-wave plate's fast and slow axes, respectively, the wave propagates along the z axis, and Ef and Es are real. The effect of the quarter-wave plate is to introduce a phase shift term eiΓ =eiπ/2 = i between the f and s components of the wave, so that upon exiting the crystal the wave is now given by

When the diameter of the airy disk's central peak becomes large relative to the pixel size in the camera (or maximum tolerable circle of confusion), it begins to have a visual impact on the image. Once two airy disks become any closer than half their width, they are also no longer resolvable (Rayleigh criterion).

Fraunhofer diffraction

Camera Type Digital SLR with CF of 1.6X Digital SLR with CF of 1.5X Digital SLR with CF of 1.3X Digital SLR with 4/3" sensor 35 mm (full frame) Digital compact with 1/3" sensor Digital compact with 1/2.3" sensor Digital compact with 1/2" sensor Digital compact with 1/1.8" sensor Digital compact with 2/3" sensor Digital compact with a 1" sensor APS 6x4.5 cm 6x6 cm 6x7 cm 5x4 inch 10x8 inch

Light rays passing through a small aperture will begin to diverge and interfere with one another. This becomes more significant as the size of the aperture decreases relative to the wavelength of light passing through, but occurs to some extent for any aperture or concentrated light source.