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achromatic doublet

Aberrations; a lecture in Optics.

Lecture-I; delivered 24-1-2017

This lecture has been¬†delivered in one of the honors class I am teaching this semester. You will do really well to read the linked article on Optical path and Fermat’s Principle which is not not intended as a honors lecture.

Optical systems are studied under two assumptions:

Object point does not lie far away from the axis of the optical system.

Rays taking part in image formation make a small angle with the axis of the optical system.

The domain of optics where above two assumptions are valid is called as Paraxial optics. Paraxial systems are highly idealized and in reality do not perfectly represent the situation. The consequential errors in image reconstruction are known as aberrations. The paraxial assumption can be represented by truncating at the first term of the polynomial expansion of the sin function by the Maclaurin series. 

If instead the 2nd term in the Maclaurin series retained and higher order terms are truncated then we say it’s a 3rd order theory — as opposed to the 1st order theory which we called the paraxial optical assumption. If a single wavelength source of light is considered along with a 3rd order theory the deviations from 1st order theory results thus obtained are summed up as primary or monochromatic aberrations. These aberrations are also known as Seidel aberrations in accordance with the name of the scientist Ludwig Von Seidel who studied them.

Thus these primary aberrations are broadly categorized into 5 types;

Spherical aberration
Coma
Astigmatism
Petzval field curvature
Distortion

The first 3 type of aberration lead to a deterioration in the quality of the image making them unclear. The last 2 types cause deforming of the shape or size of the images.

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