Excellent video Joel. I have a small comment regarding the maximum angle of the reference beam, Fourier domain aliasing, and needing a beam splitter to physically get the reference in there. You mention that higher spatial frequencies due to a too large angle of the reference beam cannot be resolved and thus will remove the fringes. This is not true. What will actually happen is that the interference pattern between reference and signal aliases back to a lower frequency. Thus, if you accept this aliasing, you can support a reference beam with larger angle, giving you more physical space and freedom to work with. In our lab we have a camera supporting ~1.5 degrees and inject the reference beam at ~5 degrees horizontally to give us some more space. This allows us to measure without a beam splitter, decreasing PDL of the measurement apparatus. The vertical angle we use is not aliased and within the angular limits you calculate in the video.
Don't you lose a lot of fringe contrast and hence reconstructed field power though? If you've got multiple fringes per pixel, the camera pixel integrates that whole area containing many fringes together in a single bucket, and it gets washed out? e.g. like this th-cam.com/video/YlKJPMQ62Sw/w-d-xo.html
@@joelacarpenter Yeah that's true, contrast gets a bit lower, so we are looking into ways to alias it fewer times. Right now our angle is ~3.8 degrees and thus aliased twice. We hope to get that down to a single alias or none at all. However, our camera has 14 bit resolution (I think) so we can tolerate some lost contrast. Plus the digital demultiplexing with specific modes acts like a matched filter, further reducing noise. For us, using a polarization-diverse DH setup, the added PDL of a generic Thorlabs beamsplitter is a bit annoying when characterizing photonic lanterns. Also, the beamsplitter introduces a lot of reflections, despite its AR coating, so getting rid of those made alignment easier. Previously with beamsplitter, we saw many aliased lower intensity interferences when we upped the power. Those are gone now.
In your MPLC setup, you didn't mention a 2f system (a Fourier lens) is used to move the flat phase surface of the output HG mode (beam waist) to the CCD sensor surface. The signal is ideal to have flat phase surface on the CCD (where we generate the hologram) because after amplitude and phase extraction, we can do overlap integral directly with the reference modes without any necessary digital propagation.
For us, we normally collimate the HG modes onto the camera as best we can, but we often don't mind if the camera isn't exactly at the collimated waist (e.g. if you can't physically get the camera to that position). If you need to propagate to a different plane, other than where the camera physically is, you could still overlap with the HG modes on the camera plane, and then phase shift each HG coefficient by the Gouy phase corresponding to what plane you want to shift too. Amplitude of the HG modes don't change in free-space propagation, you just get a phase shift. So you should be able to get away with not digital propagating the fields and then overlapping. Rather, you overlap, then digitally propagate the coefficients themselves by phase shift. In the digHolo library I wrote, there's actually an option for setting your own basis transformation matrix. So if you wanted to convert HGs in the camera plane, to HGs in some other plane, you could feed in an identity-like matrix, with phase-shift along the diagonal to shift each HG mode into a different plane.
@@joelacarpenter Thank you Joel! I write down the HG mode equation and at a propagation distance z, I did found the phase difference goes with different mode components is just the Gouy phase. The quadratic phase delay and constant phase delay are common factors for all mode components. As a result, as you said, we only need to multiply the coefficients by the corresponding Gouy phase. And I have a small comment on your reply: amplitudes of the HG modes reduce as beam propagates. But the shape of the eigenmodes preserve.
@@joelacarpenter zwhat exactly do you mean by conjugate of the waves between 15:20-16:00 of the wave..like a complex conjugate or the different phase term?
I assume the reconstruction field is complex valued, and the phase information is contained in the argument and the intensity in the modulus, is this correct? If so, in case one takes the magnitude of the reconstruction, one would simply end up with the intensity of the original image field as if holography was never performed (but with 1/3 resolution), and loses all phase information? I just wanted a sanity check. Thank you
Don't follow what you're asking. But there's two examples shown, one where you're optimising for a desired intensity distribution (and you don't care about the phase), and another example where you care about both amplitude and phase in a certain region, but don't care what happens outside that region. In both cases, you're reinforcing the aspect and/or region of the field you want, and letting some other aspect change (such as the phase) to let the aspect you want get optimised. If you end up in a situation where you've thrown away everything in one of the planes (i.e. both amplitude and phase everywhere in the plane), then you've done something wrong. There's always some bit you change, and some bit that you let stay whatever it already is.
I made my own script for that. It's basically just the hsv colormap for the phase, multiplied by the normalised amplitude of the thing you're plotting. i.e. a hsv colormap for the phase, which fades to black depending on the amplitude information.
Wonderful tutorial, and very clearly presented!
Excellent video Joel. I have a small comment regarding the maximum angle of the reference beam, Fourier domain aliasing, and needing a beam splitter to physically get the reference in there. You mention that higher spatial frequencies due to a too large angle of the reference beam cannot be resolved and thus will remove the fringes. This is not true. What will actually happen is that the interference pattern between reference and signal aliases back to a lower frequency. Thus, if you accept this aliasing, you can support a reference beam with larger angle, giving you more physical space and freedom to work with. In our lab we have a camera supporting ~1.5 degrees and inject the reference beam at ~5 degrees horizontally to give us some more space. This allows us to measure without a beam splitter, decreasing PDL of the measurement apparatus. The vertical angle we use is not aliased and within the angular limits you calculate in the video.
Don't you lose a lot of fringe contrast and hence reconstructed field power though? If you've got multiple fringes per pixel, the camera pixel integrates that whole area containing many fringes together in a single bucket, and it gets washed out? e.g. like this th-cam.com/video/YlKJPMQ62Sw/w-d-xo.html
@@joelacarpenter Yeah that's true, contrast gets a bit lower, so we are looking into ways to alias it fewer times. Right now our angle is ~3.8 degrees and thus aliased twice. We hope to get that down to a single alias or none at all. However, our camera has 14 bit resolution (I think) so we can tolerate some lost contrast. Plus the digital demultiplexing with specific modes acts like a matched filter, further reducing noise. For us, using a polarization-diverse DH setup, the added PDL of a generic Thorlabs beamsplitter is a bit annoying when characterizing photonic lanterns. Also, the beamsplitter introduces a lot of reflections, despite its AR coating, so getting rid of those made alignment easier. Previously with beamsplitter, we saw many aliased lower intensity interferences when we upped the power. Those are gone now.
Thank you for the great tutorial!
In your MPLC setup, you didn't mention a 2f system (a Fourier lens) is used to move the flat phase surface of the output HG mode (beam waist) to the CCD sensor surface. The signal is ideal to have flat phase surface on the CCD (where we generate the hologram) because after amplitude and phase extraction, we can do overlap integral directly with the reference modes without any necessary digital propagation.
For us, we normally collimate the HG modes onto the camera as best we can, but we often don't mind if the camera isn't exactly at the collimated waist (e.g. if you can't physically get the camera to that position). If you need to propagate to a different plane, other than where the camera physically is, you could still overlap with the HG modes on the camera plane, and then phase shift each HG coefficient by the Gouy phase corresponding to what plane you want to shift too. Amplitude of the HG modes don't change in free-space propagation, you just get a phase shift.
So you should be able to get away with not digital propagating the fields and then overlapping. Rather, you overlap, then digitally propagate the coefficients themselves by phase shift.
In the digHolo library I wrote, there's actually an option for setting your own basis transformation matrix. So if you wanted to convert HGs in the camera plane, to HGs in some other plane, you could feed in an identity-like matrix, with phase-shift along the diagonal to shift each HG mode into a different plane.
@@joelacarpenter Thank you Joel! I write down the HG mode equation and at a propagation distance z, I did found the phase difference goes with different mode components is just the Gouy phase. The quadratic phase delay and constant phase delay are common factors for all mode components. As a result, as you said, we only need to multiply the coefficients by the corresponding Gouy phase.
And I have a small comment on your reply: amplitudes of the HG modes reduce as beam propagates. But the shape of the eigenmodes preserve.
@@joelacarpenter zwhat exactly do you mean by conjugate of the waves between 15:20-16:00 of the wave..like a complex conjugate or the different phase term?
@@leif1075 yep, complex conjugate
I assume the reconstruction field is complex valued, and the phase information is contained in the argument and the intensity in the modulus, is this correct? If so, in case one takes the magnitude of the reconstruction, one would simply end up with the intensity of the original image field as if holography was never performed (but with 1/3 resolution), and loses all phase information? I just wanted a sanity check. Thank you
Don't follow what you're asking. But there's two examples shown, one where you're optimising for a desired intensity distribution (and you don't care about the phase), and another example where you care about both amplitude and phase in a certain region, but don't care what happens outside that region. In both cases, you're reinforcing the aspect and/or region of the field you want, and letting some other aspect change (such as the phase) to let the aspect you want get optimised. If you end up in a situation where you've thrown away everything in one of the planes (i.e. both amplitude and phase everywhere in the plane), then you've done something wrong. There's always some bit you change, and some bit that you let stay whatever it already is.
Great tutorial! How do you make those amplitude intensity plots (i cant make them in matlab...)
Thank you
I made my own script for that. It's basically just the hsv colormap for the phase, multiplied by the normalised amplitude of the thing you're plotting. i.e. a hsv colormap for the phase, which fades to black depending on the amplitude information.