Fourier optics model of a 4f system

In summary, the conversation discusses representing two lenses, L1 and L2, with focal lengths of 910mm and 40mm respectively. The lenses are spaced apart by f1+f2 and a unit amplitude plane wave is incident on L1. The goal is to find the resulting irradiance pattern after passage through both lenses. The speaker mentions using Fourier transforms, specifically the Fraunhofer diffraction integral, for L1 with z=f1. However, there is uncertainty on how to handle L2 and whether an inverse version of the Fraunhofer diffraction integral is needed while accounting for the focal length f2.
  • #1
Skaiserollz89
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TL;DR Summary
I am attempting to model a 4f system in matlab. However, before I do I want to ensure I am understanding the fourier optics involved in doing so.
In my system I am trying to represent two lenses. L1 with focal length f1=910mm and the other lens, L2 with focal length f2=40mm. These lenses are space such that there is a distance of f1+f2 between the lenses. I have a unit amplitude plane wave incident on L1. My goal is to find the resulting irradiance pattern after passage through both lenses.

I think I only need to perform a couple fourier transforms. For L1, I will use the Fraunhofer diffraction integral on the incoming field u_in(x,y) with z=f1. This results in the transform field U_in(fx,fy) at f1. From here I'm not sure what to do. For lens L2 do I need to do an inverse version of the Fraunhofer diffraction integral to get out of frequency space while simultaneously accounting for the focal length of the 2nd lens f2? Any advice would be much appreciated!
 
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  • #2


The Fourier optics model of a 4f system is a powerful tool for analyzing optical systems with multiple lenses. In your system, you have two lenses, L1 and L2, with focal lengths of 910mm and 40mm respectively. These lenses are spaced such that there is a distance of f1+f2 between them. To find the resulting irradiance pattern after passage through both lenses, you are correct in saying that you will need to perform a couple of Fourier transforms.

First, for L1, you will need to use the Fraunhofer diffraction integral on the incoming field u_in(x,y) with z=f1. This will result in the transformed field U_in(fx,fy) at f1. This transformed field will then act as the input for L2. However, in order to properly account for the focal length of L2, you will need to use the inverse version of the Fraunhofer diffraction integral. This will allow you to transform the field back into real space and account for the focal length of L2 at the same time.

Once you have performed the inverse transform, you will have the field at the focal plane of L2. From here, you can use the standard thin lens equation to determine the field at the final image plane. This will give you the resulting irradiance pattern after passage through both lenses.

In summary, to find the resulting irradiance pattern in your system, you will need to perform two Fourier transforms and use the inverse version of the Fraunhofer diffraction integral to properly account for the focal length of L2. This will allow you to accurately analyze the behavior of your 4f system and determine the resulting irradiance pattern.
 

1. What is a Fourier optics model of a 4f system?

A Fourier optics model of a 4f system is a mathematical representation of an optical system that uses the principles of Fourier analysis to describe the propagation of light through the system. It consists of two lenses separated by a distance of 4 times their focal length, hence the name "4f system".

2. What are the key components of a Fourier optics model of a 4f system?

The key components of a Fourier optics model of a 4f system are two lenses, an input plane, an output plane, and a Fourier transform plane. The input plane is where the light enters the system, the lenses focus and manipulate the light, and the output plane is where the final image is formed. The Fourier transform plane is where the Fourier transform of the input light is generated.

3. How does a Fourier optics model of a 4f system work?

In a Fourier optics model of a 4f system, the input light is first transformed into a Fourier spectrum at the Fourier transform plane. This spectrum is then manipulated by the lenses to produce the desired output at the output plane. The Fourier transform property allows for precise control and manipulation of the input light, making it a powerful tool in optical systems.

4. What are the advantages of using a Fourier optics model of a 4f system?

One of the main advantages of using a Fourier optics model of a 4f system is its ability to manipulate and control light with high precision. This makes it useful in a wide range of applications, such as microscopy, imaging, and signal processing. It also allows for the correction of aberrations and distortions in the input light, resulting in a clearer and more accurate output.

5. Are there any limitations to a Fourier optics model of a 4f system?

While a Fourier optics model of a 4f system has many advantages, it also has some limitations. One limitation is that it assumes the input light is monochromatic, meaning it has a single wavelength. This makes it less effective for polychromatic light sources, such as white light. Additionally, the lenses used in the system must be of high quality and precision, as any imperfections can affect the output image.

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