# 4 Lens optical system/fourier transform

• dimestorelaser
In summary, the question is asking for the distance "z" needed to satisfy a FOURIER TRANSFORM condition between planes P1 and P3 in an optical system consisting of 4 lenses with a focal length of f and a total length of 8z. This is equivalent to finding the imaging condition between planes P1 and P5, but is an easier problem. The output represents two possible solutions and their significance in the system. Posting the image and showing attempted solutions can help in getting more specific assistance.
dimestorelaser
Question on my study guide:

An optical systems consists of 4 lenses spaced apart. Each lens has a focal length f. Each lens is located a distance "z" away from each plane as shown. The total length of the system is 8z.

Find the distance z needed to satisfy a FOURIER TRANSFORM condition between planes P1 and P3. This is equivalent to finding the imaging condition between planes P1 and P5, but is an easier problem to do. Note that there should be 2 answers. Discuss what the output represents for each of these systems.

Some direction and help on this problem would be beneficial.

The problem comes with an image. P1 is plane 1 and is located before the first lens ...there is a plane between each lens for a total of 5.

Its supposed to be easy, I am just having trouble with it. Thanks!

Hello laser, and welcome to PF.
I feel sorry you get so little response. Let me explain: When you click "New Thread" you get a template and some hints to get response. Helpers are brainwashed to not help unless posters comply. If you want more hints, click here

In your case posting the image might help. Showing what you've tried is indispensable. If you don't know where to start, do something and get stuck, so we can estimate what kind of assistance you need. Or: find an easier problem to start with.

## 1. What is a 4 Lens optical system?

A 4 Lens optical system is a type of optical setup that uses four lenses in a specific configuration to manipulate the path of light. This system is commonly used in microscopy and imaging applications.

## 2. How does a 4 Lens optical system work?

In a 4 Lens optical system, the first lens collects and collimates the light, the second lens focuses the light onto a small aperture, the third lens expands the beam and the fourth lens focuses the expanded beam onto the sample. The Fourier transform of the sample can then be calculated by analyzing the diffraction pattern of the light passing through the sample.

## 3. What is the purpose of a Fourier transform in a 4 Lens optical system?

The Fourier transform in a 4 Lens optical system is used to analyze the diffraction pattern of the light passing through the sample. This allows for the calculation of the spatial frequencies present in the sample, which can then be used to reconstruct an image of the sample.

## 4. What are the advantages of using a 4 Lens optical system?

One of the main advantages of a 4 Lens optical system is its ability to produce high-resolution images with minimal aberrations. It also allows for a large field of view and can be easily adapted for different imaging techniques.

## 5. How is a 4 Lens optical system different from other optical systems?

A 4 Lens optical system differs from other systems in the number and arrangement of lenses used. It also differs in its specific use for Fourier transform analysis, which allows for high-resolution imaging and analysis of spatial frequencies in a sample.

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