All Questions
10
questions
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84
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I don't understand intuitively why the instantaneous frequency is obtained by calculating the time derivative of the phase
I don't understand intuitively why the instantaneous frequency is obtained by calculating the time derivative of the phase
- 11
0
votes
2
answers
284
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Understanding the Fourier transform of a signal already with amplitude and phase information
I'm from an image processing background and am working my way into optics. I'm working on phase retrieval problems, trying to understand the Gerchberg-Saxton algorithm. I found this video which is ...
- 101
1
vote
2
answers
411
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How can we show that a lens is a low pass filter?
I understand from the derivation in Goodman Chapter 6 that a lens Fourier transforms light from the front focal plane onto the back focal plane, ignoring aperture effects. I've also read that a lens ...
- 1,356
1
vote
1
answer
43
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What is the relation between the frequency vector and the Nyquist frequency?
When trying to comprehend the concept of Nyquist frequency in FFT, I came across the following definition for half of the frequency range:
$$f = -f_{n}/2:df:f_{n}/2-1;$$
where $f$ represents the ...
- 753
0
votes
0
answers
126
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How can the Fourier delta function produce different matrices in single-pixel imaging?
The pattern in the masks used for single-pixel imaging are created applying equation $(1)$,
$$P_\phi (x,y) = \frac{1}{2} \left[ 1 +| F^{-1} \{\delta_H (u,v) e^{i\phi}\}|\right], \tag{1}$$
in which the ...
- 753
0
votes
0
answers
42
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What distribution shape does this broadband signal have if the bandwidth changes?
In the Lumerical tool, I'm simulating a setup using a broadband dipole signal. It is (or should be) centered at $\lambda=$ 922.5 nm and has various bandwidths $\Delta \lambda$ for different ...
4
votes
1
answer
379
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Fractional Fourier Transform and Fresnel Propagation
I am currently trying to wrap my head around Fresnel propagation, and I understand it is mathematically linked to the Fractional Fourier Transform, but I'm having a hard time with the units and the ...
- 41
1
vote
0
answers
1k
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Fraunhofer diffraction problem in Python: How to interpret discrete Fourier transform (DFT) spectrum?
I have a periodic phase grating consisting of lenslets along the x-direction, invariant in y. I want to use python to calculate the far-field (Fraunhofer) diffraction pattern that one gets when ...
- 19
0
votes
2
answers
4k
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What is a "Fourier transform limited pulse"?
I have some doubts about the definiton of a Fourier transform limited pulse. For example if I consider a generic pulse:
$$E(z,t)=\frac{1}{\sqrt{2\pi}}\int_{-\infty}^{+\infty}A(\omega)e^{i(-\beta(\...
- 768
4
votes
1
answer
1k
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Image Reconstruction:Phase vs. Magnitude
Figure 1.(c) shows the Test image reconstructed from MAGNITUDE spectrum only. We can say that the intensity values of LOW frequency pixels are comparatively more than HIGH frequency pixels.
$$
f(x,y)=...
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