Interestingly, in matlab2023b if you create the aperture with even number of pixels you do not have a linear phase, but you do with odd number of pixels. Opposite of what this video shows.
At 13:09 , why did you ignore the 1/lambda*z term when you calculated the fresnel propagated field? And why didn't you take the abs^2 when presenting it?
I ignored the factor 1/lambda*z because it's a global factor that is typically uninteresting since it doesn't change the 'shape' of the field. We typically plot the field amplitude/intensity in arbitrary or normalized units anyway. I didn't calculate the intensity by taking the squared modulus, because then lots of subtle features tend to become much less visible in the plot. So it's basically just a plotting trick (just like you can plot the log to make weak features visible), but you're right that the squared modulus would be the physical quantity that a camera would measure.
I really want to understand how to code angular spectrum propagation for reconstruction of inline lens less hologram, and how programmatically I can remove twin image which appears in reconstructed / refocus image. I love the way you explain these concepts. Please make more videos for inline lens less hologram, numerical reconstruction method, and how to develop these programs using python or MATLAB. Thank you so much for sharing your knowledge with the community. Keep up the good work.
Lectures are so helpful. Would be great to see treatment of phase-only holograms such as produced by a spatial light modulator - "kinoform", I believe. Would like to projected a "resolved" intensity pattern at intermediate ranges. Can one back propagate to determine the need phase on the SLM or is too much information missing?
When performing Fourier transforms, phase information is typically much more important than amplitude information. A common demonstration is the following: take some image or piece of music, Fourier transform it, discard amplitude information (so only keep phase), and inverse Fourier transform it. The resulting image or piece of music is still well recognizable, though somewhat degraded in quality. Since the propagation of optical fields is described by Fourier transforms (i.e. Angular Spectrum Method, Fresnel integral, Fraunhofer integral; I have another video on that ua-cam.com/video/Y5DagMbPEGk/v-deo.html ) , the same result holds: if you back-propagate a field, only keep its phase, and forward-propagate it, then the original field should be recognizable, though there will likely be additional speckle noise present. To minimize the noise, one could use iterative algorithms to optimize the phase-only hologram, see e.g. doi.org/10.1016/j.optcom.2018.09.076 (used search key words: beam shaping Gerchberg-Saxton).
@@SanderKonijnenbergThanks. Yes seems like an iterative method would be needed. Will have to ping on a colleague who was Feinig's grad student. Currently we project a pattern in the far field by imposing the FFT of a random pattern on our SLM. It does a pretty good job, except for the resulting random speckle in the far field.
I'm assuming you're talking about 12:14? The reason is that experimentally you can only measure intensity, not the complex field, directly. So in inline holography, you can only computationally backpropagate the intensity to find an approximate reconstruction of the object. Indeed, because you're not backpropagating the complex field, the reconstruction contains noticeable artefacts. Also see 8:00 of ua-cam.com/video/on9L1EAnWC4/v-deo.html .
@@SanderKonijnenberg I am talking about the object i.e. the intensity matrix (O) in your code. O is a grayscale image containing intensity information on 0-255 scale. For recording the gabor inline hologram, the object(Transparency having a transmittance matix of form 1.-t[i,j], t[i,j]
@@sudhanshushrivastava5-year886 The matrix O is intended to be the object transmission function. In this case I chose it to be real-valued and positive (which intensity is as well), but it doesn't have to be. If O is illuminated with a plane wave at normal incident, then the transmitted field U is simply O, which thus represents a complex-valued field, but its phase happens to be constant in this case.
Sorry for the late response, I've been working on some lecture notes which took me some time. I've shared them with several MATLAB codes here: drive.google.com/drive/folders/1C19nI8QTyyVAysR-pDcoJ27p6VQyVcPM?usp=sharing
Interestingly, in matlab2023b if you create the aperture with even number of pixels you do not have a linear phase, but you do with odd number of pixels. Opposite of what this video shows.
Yes, I noticed the same thing some time after I had uploaded this video. Oh well...
Thank you for this video. I needed a quick refresher and this was perfect!
At 13:09 , why did you ignore the 1/lambda*z term when you calculated the fresnel propagated field? And why didn't you take the abs^2 when presenting it?
I ignored the factor 1/lambda*z because it's a global factor that is typically uninteresting since it doesn't change the 'shape' of the field. We typically plot the field amplitude/intensity in arbitrary or normalized units anyway.
I didn't calculate the intensity by taking the squared modulus, because then lots of subtle features tend to become much less visible in the plot. So it's basically just a plotting trick (just like you can plot the log to make weak features visible), but you're right that the squared modulus would be the physical quantity that a camera would measure.
I really want to understand how to code angular spectrum propagation for reconstruction of inline lens less hologram, and how programmatically I can remove twin image which appears in reconstructed / refocus image. I love the way you explain these concepts. Please make more videos for inline lens less hologram, numerical reconstruction method, and how to develop these programs using python or MATLAB. Thank you so much for sharing your knowledge with the community. Keep up the good work.
Hii, Really nice video !!!! these methods of propagation are for free space??
Yes, isotropic media, constant refractive index
Lectures are so helpful. Would be great to see treatment of phase-only holograms such as produced by a spatial light modulator - "kinoform", I believe. Would like to projected a "resolved" intensity pattern at intermediate ranges. Can one back propagate to determine the need phase on the SLM or is too much information missing?
When performing Fourier transforms, phase information is typically much more important than amplitude information. A common demonstration is the following: take some image or piece of music, Fourier transform it, discard amplitude information (so only keep phase), and inverse Fourier transform it. The resulting image or piece of music is still well recognizable, though somewhat degraded in quality.
Since the propagation of optical fields is described by Fourier transforms (i.e. Angular Spectrum Method, Fresnel integral, Fraunhofer integral; I have another video on that ua-cam.com/video/Y5DagMbPEGk/v-deo.html ) , the same result holds: if you back-propagate a field, only keep its phase, and forward-propagate it, then the original field should be recognizable, though there will likely be additional speckle noise present. To minimize the noise, one could use iterative algorithms to optimize the phase-only hologram, see e.g. doi.org/10.1016/j.optcom.2018.09.076 (used search key words: beam shaping Gerchberg-Saxton).
@@SanderKonijnenbergThanks. Yes seems like an iterative method would be needed. Will have to ping on a colleague who was Feinig's grad student. Currently we project a pattern in the far field by imposing the FFT of a random pattern on our SLM. It does a pretty good job, except for the resulting random speckle in the far field.
The angular spectrum of a wave is the fourier transform of the complex amplitude function of the wavefield, then why did you take fft of intensity?
I'm assuming you're talking about 12:14? The reason is that experimentally you can only measure intensity, not the complex field, directly. So in inline holography, you can only computationally backpropagate the intensity to find an approximate reconstruction of the object. Indeed, because you're not backpropagating the complex field, the reconstruction contains noticeable artefacts. Also see 8:00 of ua-cam.com/video/on9L1EAnWC4/v-deo.html .
@@SanderKonijnenberg I am talking about the object i.e. the intensity matrix (O) in your code. O is a grayscale image containing intensity information on 0-255 scale. For recording the gabor inline hologram, the object(Transparency having a transmittance matix of form 1.-t[i,j], t[i,j]
@@sudhanshushrivastava5-year886 The matrix O is intended to be the object transmission function. In this case I chose it to be real-valued and positive (which intensity is as well), but it doesn't have to be. If O is illuminated with a plane wave at normal incident, then the transmitted field U is simply O, which thus represents a complex-valued field, but its phase happens to be constant in this case.
@@SanderKonijnenberg Thanks, I get it now, I'm curious how the physical extent of the object relates to that of the hologram.
Where can I find the matlab code used in this video? Thanks!
Sorry for the late response, I've been working on some lecture notes which took me some time. I've shared them with several MATLAB codes here: drive.google.com/drive/folders/1C19nI8QTyyVAysR-pDcoJ27p6VQyVcPM?usp=sharing
@@SanderKonijnenbergThx a lot. Your video lecturing is far better than I was taught in class