Visibility in Optics: Integration help

In summary, to calculate the visibility of a non point source interference pattern, you need to integrate the equation dI = (C/w)(cos^2[(ud/gL)(y-y_0)]).dy_0 between w/2 and -w/2, where C, u, d, g, l, and y are constants. This can be simplified by using the identity cos^2{x} = \frac{1}{2}(\cos{2x} +1) and evaluating the integral \int_{-w/2}^{w/2} A\cos^2{\left(B(y-y_0)\right)} \, dy_0, where A and B are constants. Further assistance can
  • #1
Master J
226
0
In calculating the visibility of an non point source interfernce pattern, you integrate the following:

dI = (C/w)(cos^2[(ud/gL)(y-y_0)]).dy_0.

between w/2 and -w/2. C, u, d, g, l , y constants.

I'm finding this pretty tricky to integrate. Could someone help? Step by step would be really helpful.
 
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  • #2
Hi Master J,
Master J said:
In calculating the visibility of an non point source interfernce pattern, you integrate the following:

dI = (C/w)(cos^2[(ud/gL)(y-y_0)]).dy_0.

between w/2 and -w/2. C, u, d, g, l , y constants.

I'm finding this pretty tricky to integrate. Could someone help? Step by step would be really helpful.
As you have it written (and assuming you mean to say that "L" is a constant), this just amounts to evaluating [tex]\int_{-w/2}^{w/2} A\cos^2{\left(B(y-y_0)\right)} \, dy_0[/tex] for constants y, A and B. Then, using a substitution, this amounts to integrating [tex]\cos^2{x}[/tex]. To do that, use the identity [tex]cos^2{x} = \frac{1}{2}(\cos{2x} +1)[/tex]. Show your work so we know where abouts you're getting stuck.
 

1. What is visibility in optics?

Visibility in optics refers to the ability of an object or image to be seen or perceived by the human eye. It is a measure of how easily an object can be distinguished from its surrounding background.

2. How is visibility measured in optics?

Visibility in optics is typically measured using a visibility index, which is calculated by comparing the brightness or contrast of an object to its surrounding background.

3. What factors affect visibility in optics?

There are several factors that can affect visibility in optics, including lighting conditions, the size and shape of the object, the color and contrast of the object, and any obstructions or interference in the viewing environment.

4. How can visibility in optics be improved?

Visibility in optics can be improved by optimizing lighting conditions, using high-contrast colors and patterns, and minimizing obstructions or interference in the viewing environment.

5. Why is visibility important in optics?

Visibility is important in optics because it affects how well an object or image can be perceived and understood by the human eye. It is particularly important in fields such as microscopy, astronomy, and imaging, where clear visibility is crucial for accurate analysis and interpretation of data.

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