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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 qR cannot be resolved.

The inspection is typically performed by trained and certified personnel, such as optical engineers or technicians, who have a thorough understanding of the specifications and requirements outlined in MIl-PRF-13830. It is important to have qualified individuals perform the inspection to ensure accurate and reliable results.

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qR is the angular position of the first order diffraction minimum (the first dark ring) l 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.

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

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If a mirror does not meet the requirements outlined in MIl-PRF-13830, it is considered non-conforming and should not be used in military applications. The manufacturer may be required to make adjustments or improvements to the mirror to bring it into compliance with the specification before it can be approved for use.

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.

Circular apertures produce diffraction patterns with circular symmetry. Mathematical analysis gives the equation,

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The key characteristics that are inspected in accordance with MIl-PRF-13830 include surface flatness, surface quality, reflective coating adhesion, and reflective coating uniformity. These characteristics are crucial in determining the overall performance and reliability of the mirror.

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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.

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,

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

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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.

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

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

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The inspection process for MIl-PRF-13830 involves visual and mechanical inspections, as well as testing for the key characteristics mentioned above. This includes using specialized equipment such as interferometers and spectrophotometers to measure and evaluate the mirror's performance.

MIl-PRF-13830 is a military performance specification that outlines the requirements and procedures for the inspection of optical mirrors used in military applications. It is important because it ensures that the mirrors meet the necessary quality and performance standards for use in critical military operations.

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.

The path difference between the direct beam and the first-order diffracted beam is exactly one wavelength, l. So,