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What isgratingelement

Damage to the microscopic groove profile is, unfortunately, irreversible; the epoxy layer, like molding clay, will retain a permanent imprint. Contamination of the grating surface with finger oils, moisture, vacuum pump oil, &c is also often permanent, particularly if the contaminated grating surface has been irradiated. If you have a damaged or contaminated grating, contact us to ask for advice, or to have us clean and inspect your grating.

While this damage may be apparent upon looking that the grating, it is not straightforward to determine the effect this damage has on the performance of the grating. Often the area affected by damage or contamination is a small fraction of the total area of the grating. Therefore, only a small portion of the total number of grooves under illumination may be damaged, displaced or contaminated. A damaged or contaminated region on the surface of a grating may have little, if any, noticeable effect on the performance of the optical system because, a diffraction grating is usually used as an integrating optic (meaning that all light of a given wavelength diffracted from the grating surface is brought to focus in the spectral order of interest). In contrast, a lens or mirror that does not focus (say, an eyeglass lens or a bathroom mirror) will show a distortion in its image corresponding to the damaged region of the optic. This familiar experience – the annoying effect of a chip on an eyeglass lens or a smudge on a bathroom mirror – has led many to assume that a similar defect on the surface of a grating will lead to a similar deficiency in performance. The most appropriate performance test of a grating with surface damage or cosmetic defects is not visual inspection but instead to use the grating in its optical system and determine whether the entire system meets its specifications.

Transmissiongrating

If the beam is abberated, for example by a poorly manufactured lens, then the beam will not have perfectly spherical converging wavefronts, and the resulting focal spot will be spread out over a larger area. The magnitude of these abberations is what determines the resolution of an optical system when it is not diffraction limited.

A diffraction grating is a first surface optic, so its surface cannot be touched or otherwise come in contact with another object without damaging it and perhaps affecting its performance. Damage can take the form of contamination (as in the adherence of finger oils) or distortion of the microscopic groove profile in the region of contact. This Technical Note describes the reasons why a grating must be handled carefully and provides guidelines for doing so.

Diffractiongratingpattern

The size of the diffraction limited spot is a function of the f-number at the image plane. So, if you know the beam diameter after the last lens element, and the back focal distance, you can compute the diffraction limited spot size just like you would for any other lens.

In the spot diagrams of optic designs the ray aberrations are always compared to the size of diffraction limited spot. In order to do this you have to find the smallest aperture in your system. This can be a deliberately placed mechanical aperture but it can also be the circumference of a lens.

Since the groove profile is maintained by the epoxy layer, rather than the reflective (metallic) coating on top of it, protective coatings such as those that meet the military specification MIL-M-13508 (regarding first-surface aluminum mirrors) do not serve their intended purpose. Even if the aluminum coating itself were to be well-protected against contact damage, it is too thin to protect the softer epoxy layer underneath it. Even "fully cured" epoxy is not very hard, resembling molding clay in its resistance to contact damage. Consequently gratings are not provided with contact-protecting coatings.

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Reflectiongrating

Supposed a lens arrangement is prepared where light from an object is collimated, focused and recollimated etc. before entering a CCD array. Given that we can calculate the diffraction-limited resolution for each lens in the system, how do we measure the diffraction limited resolution for the whole setup?

A perfectly collimated beam (with perfectly planar wavefront) passing through a perfect lens would come out of the lens with perfectly spherical wavefront, and all of the rays in the beam would be converging to a single point. In this case, the spot size is determined solely by the angle occupied by the converging cone of light*. This is what we call "diffraction limited."

Diffractiongratingformula

I read a nice discussion about this topic a while ago but can't remember which book it was in. I tried to implement it in a raytracer. It involved an iteration over all apertures in the optical train. One had to trace all apertures into the image and chose which one produced the smallest opening angle.

Diffractiongratingdiagram

If contaminants remain, try using spectroscopic-grade solvents; the purity of such solvents should be ascertained before use, and only the purest form available used. The use of carbon dioxide (CO2) snow, which reaches the grating surface in a sublimed state and evaporates, carrying with it the contaminants, has also been used with some success. The key to cleaning a grating surface is to provide no friction (e.g., scrubbing) that might damage the delicate groove structure.

Sometimes surface contamination can be removed partially, and once in a while completely, using a mild unscented dishwashing liquid. Care should be taken not to apply any pressure (even gentle scrubbing) to the grating surface. Fingerprints may occasionally be removed, but more often damage the groove structure. Dust should only be removed from the grating surface using filtered air.

What isgratingin physics

Commercially available diffraction gratings are replicated optics comprised of three layers: a substrate, an epoxy layer, and (usually) a reflective coating. Each layer meets a different purpose:

*this is the case only assuming that the beam is always the same shape. In practice most beams are circular, so all we need to worry about is its diameter. If the beam is a different shape, then its diffraction limited spot size (and shape!) will change.

I copied the following spot diagram from http://www.astronomy.net/articles/17/. The black ring is the diffraction limited spot size (3.3 $\mu$m if you convert from inch) the red dots are the spot with ray aberrations. You can see a strong Coma with $1\mu$m spread in x.

Warnings against touching the grating surface notwithstanding, damage to the surface occasionally occurs. Contact from handling, mounting or packaging can leave permanent visible marks on the grating surface. Some gratings have visible surface defects. Many are cosmetic defects that one can see with the naked eye, but which do not adversely affect the performance of the grating. Also visible are occasional grooves on gratings that are ruled too lightly, known as ruling streaks. These ruling streaks also do not affect the performance of the grating. Some cosmetic defects that do not adversely impair the optical performance represent the best available quality for a grating with a particular set of specifications. For example, some gratings have 'worm tracks' due to mechanical ruling of the master grating from which the replicated grating was taken, others have coating defects like spit or spatter, and others have 'pinholes' (tiny voids in the reflective coating). The many possible classifications of surface defects and the many opportunities to render the surface permanently damaged conspire to make the surfaces of many gratings look less than cosmetically perfect.

Diffractiongratingexperiment

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I think any decent book on lens design should contain a chapter on the topic. See for example chapter 6 in Warren J. Smith: "Modern optical engineering: the design of optical systems".

I want to briefly clarify what exactly is meant when we talk about being "diffraction limited." As light is focused, it will reach some minimum spot size before it begins to expand again. The size of this spot depends on how much the light beam is distorted.

Damage to a region of grooves, or their displacement, will theoretically have some effect on the efficiency of the light diffracted from that region, as well as the total resolving power of the grating, but in practice such effects are generally not noticeable. Of more concern, since it may be measurable, is the effect surface damage may have on light scattered from the grating, which may decrease the signal-to-noise (SNR) of the optical system. Most forms of surface damage can be thought of as creating scattering centers where light that should be diffracted (according to the grating equation) is scattered into other directions instead.