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When light from the various points of a specimen passes through the objective and an image is created, the various points in the specimen appear as small patterns in the image. These are known as Airy discs. The phenomenon is caused by diffraction of light as it passes through the circular aperture of the objective.

Diffractiongratingformula

The dispersion and efficiency of a grating are dependant on the distance between adjacent grooves and the groove angle. Gratings are generally better than prisms - they are more efficient, they provide a linear dispersion of wavelengths and do not suffer from the absorption effects that prisms have which limits their useful wavelength range.

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Diffractiongratingexperiment

A diffraction grating is an optical element, which separates (disperses) polychromatic light into its constituent wavelengths (colors). The polychromatic light incident on the grating is dispersed so that each wavelength is reflected from the grating at a slightly different angle. The dispersion arises from the wavefront division and interference of the incident radiation from the periodic structure of the grating.

The wavelength of light is an important factor in the resolution of a microscope. Shorter wavelengths yield higher resolution. The greatest resolving power in optical microscopy requires near-ultraviolet light, the shortest effective visible imaging wavelength.

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Plane diffractiongrating

The numerical aperture of a microscope objective is a measure of its ability to resolve fine specimen detail. The value for the numerical aperture is given by,

θR is the angular position of the first order diffraction minimum (the first dark ring) λ is the wavelength of the incident light d is the diameter of the aperture

For resolution to occur, at least the direct beam and the first-order diffracted beam must be collected by the objective. If the lens aperture is too small, only the direct beam is collected and the resolution is lost.

where: n is the order of diffraction, λ is the diffracted wavelength d is the grating constant (the distance between successive grooves) θi is the angle of incidence measured from the normal and θd is the angle of diffraction measured from the normal. The diagram above shows the orders of the diffracted wavelength. As well as positive orders, light can also be diffracted in the opposite direction (i.e. n = -1, -2 etc.) Higher orders may also appear, but these decrease in intensity. Usually the first order lines (n=1 or n=-1) are the most intense.

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where 2α is the angle through which the first-order beam is diffracted. Since the two beams are just collected by the objective, i = α, thus the limit of resolution is,

The limit at which two Airy discs can be resolved into separate entities is often called the Rayleigh criterion. This is when the first diffraction minimum of the image of one source point coincides with the maximum of another.

Reflective diffractiongrating

Airy discs consist of small, concentric light and dark circles. The smaller the Airy discs projected by an objective in forming the image, the more detail of the specimen is discernible. Objective lenses of higher numerical aperture are capable of producing smaller Airy discs, and therefore can distinguish finer detail in the specimen.

From the equation it can be seen that the radius of the central maximum is directly proportional to λ/d. So, the maximum is more spread out for longer wavelengths and/or smaller apertures.

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Diffractiongratingformula wavelength

Numerical aperture determines the resolving power of an objective, the higher the numerical aperture of the system, the better the resolution.

Diffractiongratingpattern

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Expected spectral resolution and simultaneous bandpass are also influenced by how light is coupled into the spectrograph, the central wavelength of interest and associated grating “working angle”, as well as the detector pixel array format at the output plane. Some of these trade-offs can be assessed with the Andor resolution calculator for Kymera and Shamrock Czerny-Turner spectrographs.

DiffractiongratingPDF

The dispersed light is then re-imaged by the spectrograph and the required wavelength range is directed to a detection system. Gratings consist of equally spaced parallel grooves, formed on a reflective coating and deposited on a substrate. The shape of the grooves (blaze angle) influences what wavelength range the grating is best optimised for.

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where n is the refractive index and equal to 1 for air and α is the half angle subtended by rays entering the objective lens.

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The primary minimum sets a limit to the useful magnification of the objective lens. A point source of light produced by the lens is always seen as a central spot, and second and higher order maxima, which is only avoided if the lens is of infinite diameter. Two objects separated by a distance less than θR cannot be resolved.

Diffractiongratingdiagram

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The limit of resolution (or resolving power) is a measure of the ability of the objective lens to separate in the image adjacent details that are present in the object. It is the distance between two points in the object that are just resolved in the image. The resolving power of an optical system is ultimately limited by diffraction by the aperture. Thus an optical system cannot form a perfect image of a point.

The Andor Shamrock SR-750 is based on Czerny-Turner optical design. The Shamrock is available as a pre-aligned detector/spectrometer option allowing for seamless integration of software,…

These influence the choice of grating line density, blaze angle/wavelength, master (different masters for a given line density and blaze angle yield different efficiency and polarisation characteristics) and grating size.

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