Creating 2D Irradiance Distribution with Exact Scalar Method

It is important to note that the Gaussian function should be centered at the origin in order for this method to work properly.
  • #1
optics101
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I am trying to create (in matlab) an irradiance distribution in a 2-D array, using the exact scalar method. As of now I have a 2-D array defined as my aperture function and I also have a 2-D array defined as a Gaussian function (light source).

I believe that I know how to do this with a uniform input due to some simplifications in the mathematics, however I'm not sure how or where to include the Gaussian input. My intuition says that there should be a convolution included somewhere, but I'm not quite sure. Any help would be greatly appreciated. I'm not necessarily looking for any specific code, just the correct way to go about solving or incorporating the Gaussian source.

I am not sure if there is enough detail in this post, if not please let me know and I will post whatever more necessary.

Thanks!
 
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  • #2
The exact scalar method for creating an irradiance distribution in a 2D array consists of two steps. In the first step, you calculate the Fourier transform of the aperture function (i.e., the 2D array that defines your aperture). In the second step, you multiply the Fourier transform of the aperture function by the Fourier transform of the Gaussian function (i.e., the 2D array that defines your light source). The result of this multiplication is the desired irradiance distribution. In Matlab, this can be accomplished with the fft2 and ifft2 functions. The fft2 function can be used to calculate the Fourier transform of the aperture and Gaussian functions. The ifft2 function can be used to calculate the inverse Fourier transform of the product of the two Fourier transforms. This will give you the desired irradiance distribution.
 

1. What is the Exact Scalar Method for creating 2D irradiance distribution?

The Exact Scalar Method is a computational technique used to calculate the irradiance (intensity) of light at different points on a 2D surface. It takes into account the exact geometric and optical properties of the light source and the surface, resulting in a more accurate and realistic distribution of light compared to other methods.

2. What are the advantages of using the Exact Scalar Method?

The Exact Scalar Method has several advantages over other methods for creating 2D irradiance distributions. It takes into account the full complexity of the light source and surface, resulting in a more accurate representation of real-world conditions. It also allows for the calculation of irradiance at any point on the surface, instead of just at discrete points, providing a more detailed and comprehensive analysis.

3. What types of surfaces can the Exact Scalar Method be used on?

The Exact Scalar Method can be used on any 2D surface, including flat and curved surfaces. It can also be used on surfaces with complex geometries, such as those with multiple concave and convex regions, making it a versatile tool for many scientific and engineering applications.

4. Is the Exact Scalar Method difficult to implement?

The Exact Scalar Method can be complex and requires knowledge of optics and computational techniques. However, there are software programs and libraries available that can assist with the implementation of this method, making it more accessible for researchers and scientists.

5. How is the accuracy of the Exact Scalar Method validated?

The accuracy of the Exact Scalar Method can be validated by comparing the results to experimental data or other established computational methods. Additionally, sensitivity analyses can be performed to assess the impact of different variables on the calculated irradiance distribution. Overall, the more closely the results align with real-world observations, the more accurate the method is considered to be.

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