# Doing a research on aberrations in order to

• Septim
In summary: You can derive the third order spherical aberration formula from the equation sin(q) = q^3/3! + q^5/5!+...
Septim
Hello everyone,

I am doing a research on aberrations in order to prepare a presentation. I looked at Optics, Hecht and Introduction to Optics, Pedrotti; however, I think they use different conventions for aberrations. Is there an established standard for aberrations(I heard the name Seidel)? I also wonder what the third order aberration means; is it sine expanded to include angle cubed or the aberrations are written up to 3rd order of the aperture diameter for example. I am pretty confused about this topic and in need of a good resource which will guide me and possibly derive some of the aberration formulas explaining each one in detail. Any suggestion is appreciated.

Thanks

It is very complex topic. There is so many good books like for example Rudolf Kingslake Lens Design Fundamentals - in that book you will find detail derivation of all kinds of aberrations.

Thanks for your reply; I looked at that book but found it kind of confusing. If you have any other suggestions I would appreciate it.

Septim said:
Hello everyone,

I am doing a research on aberrations in order to prepare a presentation. I looked at Optics, Hecht and Introduction to Optics, Pedrotti; however, I think they use different conventions for aberrations. Is there an established standard for aberrations(I heard the name Seidel)? I also wonder what the third order aberration means; is it sine expanded to include angle cubed or the aberrations are written up to 3rd order of the aperture diameter for example. I am pretty confused about this topic and in need of a good resource which will guide me and possibly derive some of the aberration formulas explaining each one in detail. Any suggestion is appreciated.

Thanks

The Seidel aberrations are referred to as 'third order' because the expansion sin(q) = q + q^3/3! + q^5/5!+... has a third-order polynomial after the paraxial sin(q) ~ q approximation. There are 7 third order aberrations (piston, tilt, spherical, coma, petvzal, distortion, astigmatism), a bunch of 5th order, 7th order, etc.

Alternatively, the wavefront aberration is written in terms of Zernike polynomials- mapping a Zernike coefficient with a Seidel aberration is not possible, but there are ways to convert one to the other.

A good resource (free, etc.) is the MIL-HDBK 141 (Optical Design)

http://www.optics.arizona.edu/ot/opti502/MIL_HDBK_141.html

3rd order aberrations are in Chapter 8.

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Thanks you I will take a look at that.

I need to derive the third order spherical aberration formula for a thin lens which consists of two refracting surfaces how can I do so? I am attaching an image file containing the formula at the bottom of the page. Thanks for your help.

#### Attachments

• ss.jpg
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## What is the purpose of researching aberrations?

The purpose of researching aberrations is to understand and study deviations or abnormalities from the expected or normal behavior in a particular context. This can help identify potential issues or problems and find ways to address them.

## What are the different types of aberrations that can be studied?

There are various types of aberrations that can be studied, including chromatic aberration, spherical aberration, coma aberration, astigmatism, and distortion. These can occur in different fields of science, such as optics, genetics, and biology.

## What are the common techniques used in researching aberrations?

The most common techniques used in researching aberrations include data collection and analysis, experimental studies, computer simulations, and mathematical models. These methods allow scientists to observe and measure aberrations and understand their causes and effects.

## What are the potential applications of studying aberrations?

The study of aberrations has various potential applications, such as in improving imaging and optical systems, understanding genetic disorders, and identifying environmental issues. It can also help in the development of new technologies and treatments for aberrations.

## What are the ethical considerations in researching aberrations?

When conducting research on aberrations, it is important to consider ethical implications, such as protecting human and animal subjects, ensuring informed consent, and maintaining confidentiality of sensitive data. Additionally, researchers must adhere to ethical guidelines and regulations set by their institution and governing bodies.

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