# Optics Q : Diffraction Pattern from a Ronchi Ruling

• 300072507
In summary, the experiment was trying to measure the diffraction pattern from a Ronchi ruling and it didn't work because the Ronchi ruling doesn't have an infinite number of gratings and the slit isn't exactly a 'point source'. The problem could be fixed by taking the transform of the Fourier image of the first lens, but there is no guarantee that the equation would still work. The experiment was also done in a 4-f system.
300072507
Optics Q!: Diffraction Pattern from a Ronchi Ruling

Hey everyone,

allow me to explain the experiment I'm working on before I get into my question. The experiment has light passing through a slit at the focal point of a lens. Since the light is at the focal point, theoretically it should become collimated as it continues past the lens. The light then passes through a ronchi ruling, and through another lens. What I've done is put a CCD camera at the Fourier plane (focal point of the second lens) and taken an image. My problem is in fitting to the intensity.

Theoretically, the function I would be using to fit would be a convolution of the Fourier transform of a single square wave and a dirac comb and then squaring it. The Fourier transform of a single square wave is a sinc, and the transform of a dirac comb is approximately another dirac comb. The convolution of these gives me the electric field at the Fourier plane. Squaring obviously gives me something that is proportional to intensity.

So anyway, the fit doesn't work. My professor told me that the 2 reasons for this are: the Ronchi ruling doesn't have an infinite number of gratings, the slit isn't exactly a 'point source'. I know how to account for the being a lack of gratings, but I'm not sure how to accommodate for the slit width. I was thinking, since the slit is at the focal point of the first lens, I could take the transform of that and somehow work it into my real image equation (original equation before transform).

What happens when you rotate the Ronchi ruling with respect to the slit orientation? That should give you some clues.

Also, it sounds like you have some sort of 4-f system. Is that correct?

.

Hello,

Thank you for sharing your experiment and question with us. It sounds like you are working on a fascinating project! Diffraction patterns from Ronchi rulings are commonly studied in optics and can provide valuable insights into the properties of light and its behavior when interacting with different materials.

In regards to your question about fitting the intensity of the diffraction pattern, there are a few factors that may be affecting your results. As you mentioned, the finite number of gratings in the Ronchi ruling and the width of the slit can both contribute to deviations from the expected pattern. One way to account for the slit width is by using a Gaussian function to approximate the intensity distribution. This can be done by convolving the Fourier transform of the Gaussian with the Fourier transform of the square wave and then squaring the result to get the intensity. This approach takes into account the finite width of the slit and can improve the fit to your data.

Additionally, it may be helpful to consider other factors that could affect your results, such as aberrations in the lenses or imperfections in the Ronchi ruling. These can also contribute to deviations from the expected pattern and may need to be taken into account in your analysis.

I hope this helps and wish you the best of luck with your experiment! Keep exploring and experimenting, as that is the essence of science.

## 1. What is a diffraction pattern?

A diffraction pattern is a series of bright and dark fringes that form when light passes through a narrow slit or aperture. It is caused by the interference of light waves as they diffract or spread out after passing through the slit.

## 2. What is a Ronchi ruling?

A Ronchi ruling is a series of evenly spaced parallel lines etched onto a glass or metal plate, used for studying the diffraction pattern of light. It is named after its inventor, Italian physicist Vincenzo Ronchi.

## 3. How is a diffraction pattern from a Ronchi ruling created?

A beam of light is shone through the Ronchi ruling, causing the light to diffract and create a diffraction pattern. The number of lines per unit length on the ruling determines the spacing of the fringes in the pattern.

## 4. What information can be obtained from a diffraction pattern from a Ronchi ruling?

The diffraction pattern can be used to calculate the wavelength of the light source, as well as the size and shape of the ruling. It can also be used to study the behavior of light waves and the principles of diffraction.

## 5. What are some practical applications of studying diffraction patterns from Ronchi rulings?

Diffraction patterns from Ronchi rulings are commonly used in the field of optics, such as in the design and testing of optical instruments like telescopes and microscopes. They can also be used in quality control processes for manufacturing precision optical components.

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