If you want to get the same distribution of amplitudes and phases at SLM and at your sample, you must always produce image of SLM at the sample. At your picture you show optical scheme with double imaging (you call it 4F imaging). If you use single lens for imaging, you also obtain the required result, only image will be 180 deg. rotated. Your scheme magnification is 1. You can change magnification, if you need, but always keep imaging condition (1/F = 1/s +1/d).

Thanks for the reply. Yes now I understand. But suppose I want only phase modulation what should be my scheme like?

Hi Jitendra,

the difference is that you don't really need a 4f system for the amplitude SLM (i guess something like a digital micromirror device, or a trasmissive LCD), but you do need a 4f system for the phase.

If you have amplitude modulation, you just need to create a conjugated plane on your sample according to geometrical optics, and you can do that with a single lens, using the thin lens formula.

However, geometrically conjugated planes have the same intensity, but not the same phase!

If you have a phase only spatial light modulator (like an LCOS or a deformable mirror), you need a 4f system. In this case you are using the Fourier optics priciple stating that, if you have a given field (therefore considering both amplitude and phase) at the front focal plane of the lens, you will have its Fourier transform at the back focal plane. You can then put a second lens with its front focal plane at such Fourier transform plane, and on the back focal plane you will obtain the Fourier transform of the Fourier transform of the original field, which is equivalent to the exact same field, but mirrored on the lateral directions.

Yes. Paolo Pozzi emphasizes important detail, required for correct phase representation.

Thanks for the explanation Aleksandr A. Tarasov and Paolo Pozzi !

Jitendra, the answer really depends on what you're trying to accomplish. Most people that want to project an amplitude pattern onto a sample will put the SLM at the input of a 4f imaging system, and the sample at the output of the 4f system. However, for a phase-only SLM most people write holograms onto the SLM and the sample then goes in the focal plane of a single lens following the SLM. The holograms are generated by taking the desired amplitude pattern at the sample, and calculating the Fourier transform, then converting this full-complex pattern into phase-only using something like the Gerchberg-Saxton algorithm. With this phase-only SLM approach you can think of the SLM as more of a multi-spot beam-steering device, which means you're taking most of the light that hits the SLM and putting it where you want on the sample, versus the amplitude-only SLM which relies on polarizing optics to block the light from regions where you don't want light. Therefore the phase-only SLM is usually considerably more light efficiency.

Thanks Kipp!

I understand it clearly. I have read that it is possible to do both amplitude and phase modulation using phase only SLM . Is it really possible ? If so what should we do to acheive it ?

Yes, it is possible to modulate both phase and amplitude under certain circumstances.

Case 1 - pulse shaping or spectral shaping. The light is spread across one axis of the SLM using a prism or diffraction grating to separate the wavelengths onto different columns of the SLM. Then each column can be written with a diffraction grating, where the difference in phase between The maximum and minimum phase retardants determines the diffraction efficiency, or amplitude modulation, and the average phase of the diffraction grating determines the phase.

Case 2 - super pixel. Any complex value can be written in terms of sin and cos, therefore you can create a 2 x 2 super pixel writing the sin into the upper left and lower right pixels and cos into the upper right and lower right pixels of the super pixel. This of course cuts the available resolution in half In both axes.

Thanks Again Kipp!

Finally one more question if I want this same phase only SLM to perform amplitude modulation alone can I do it by placing a polarizer before and after SLM. Does it have to be in crossed position ?

Yes, adding polarizers before and after turn the phase into amplitude modulation, 1/2-wave phase retardance rotates polarization so input polarizer should be at 45 degrees relative to the SLM slow axis. Crossed polarizers always result in better contrast ratio than parallel polarizers, but either can be used. If using a polarizing beam splitter cube since most SLMs are reflective, then simply place a passive 1/2-wave plate between the PBS cube and the SLM in order to tune the polarization axis relative to the SLM.

Thanks a lot Kipp!!

Hi Kipp, I have few more clarifications to be made, Hope you can help me,

I am trying to shape the wavefront phase so as to focus light through a scattering medium using a phase only . For which I need to find illuminate the sample with a random phase input which varies from 0 to 2pi.

If I understand clearly the SLM is characterised for a specific wavelength(I mean which we calibrate initially) and has specific gray levels corresponding to each phase shift. So suppose I created a random phase and found the corresponding graylevel to be inserted on SLM. Then to get this random phase on my scattering medium. Is it advisable to image SLM on to the scattering medium. Does it correspond to the same phase shift I gave in terms of the graylevels to the SLM.

Essentially the calibrated SLM uses a look-up table, LUT, to convert the input pixel values to an expected phase value. When properly calibrated your input pixel values will range from 0 - 255 (assuming an 8-bit controller). The pixel value of 0 would be 0 phase, the pixel value of 255 would be 2 pi phase, and a pixel value of 127 would be 1 pi phase. It's a simple linear relationship if the calibration is performed correctly. Then, regardless of what hologram pattern you want to put on the SLM, whether it's a random phase pattern, a lens function, or a blazed grating, pixel values from 0 - 255 would always be converted in a linear fashion to phase ranging from 0 - 2 pi. Imaging the SLM onto your sample then ensures you have the desired phase pattern illuminating your sample.

Thanks Kipp! I am using HEO 1080 P Phase only SLM. Since it was an old one, I got a look uptable which was already done by someone else for 543 nm in the lab. And on the Excel file I could see that for value 255 it corresponds to 12.27 radians, (please see attached pic)

does this datasheet makes sense ? Or do you think I should consider doing the calibration from the scratch ?

Compared to the SLMs we provide at Meadowlark, the calibration curve you're working with is not very linear. It would be much simpler to use if it were properly calibrated to provide a linear, 2 pi phase response at your wavelength.

Hi Kip

One more query. While working with Phase only SLM. Is there a problem if we are taking only zero order light for phase modulation ? Or is it that we should work with +1or -1 order ?

A phase-only SLM can be used with either approach, it all depends on your particular application as to how you would implement the SLM.

Thanks. So if my requirement is just to image the SLM so as to produce random phase distribution, Then would it be fine that if I work with the zero order. Please correct me if I am wrong.

Yes, you would want to use the zero order for this particular application, and it should work quite well with a phase-only SLM.

Hi While using a phase only reflective SLM, what is the working polarization of the input laser beam ? Is it along the horizontal axis(dimensionally long axis ) or Verical Direction of the SLM ? In either cases the modulated beam gets an orthogonal polarization state if I am not mistaken ? Can someone please help me understand ?

Jitendra, most of our phase-only SLMs are manufactured with the slow-axis of the liquid crystal aligned parallel to the vertical axis. However, we also design the mount in such a way that it’s easy to rotate the SLM by 90 degrees when mounting it to your optics bench.

if the input polarization is linear and aligned parallel to the slow-axis of the liquid crystal then there will not be any polarization rotation caused by the SLM. This is the phase-only approach. However, if your input light is linear and aligned at 45 degrees to the slow-axis the output light will have a 90 degree polarization rotation whenever the pixels values are set to yield a half-wave of phase retardance. This is the amplitude-mostly approach if you follow the SLM with a polarizer that is orthogonal to the input polarization axis.

Hii Kipp,

I am working with Holoeye pluto phase only reflective SLM. I get very low diffraction efficiency in 1st order. I used blazed grating with my diffraction pattern. could you explain me how can I increase the efficiency of diffraction in particular order. I used 4F setup. Can I use zero order for Multi beam-lets generation??

Thank you in advance.

Hitesh, I have never used a Holoeye SLM. However, I have read these SLMs will result in lower diffraction efficiency due to phase flicker, which is a result of the pulse code modulation required to get gray levels with a binary SLM. The phase flicker causes light to go into locations other than the 1st-order spot determined by your blazed grating. You can verify this by measuring the diffraction efficiency with a high-speed detector and oscilloscope. If this is indeed the cause of your problem, I have also read you can reduce these issues by changing the pulse code scheme, but I do not believe you can completely eliminate the phase flicker. To completely eliminate the problem, I would recommend an SLM that uses an analog backplane, such as those made by my company, Meadowlark Optics.

Thanks Kipp. I checked your website your products are excellent.

I measured the diffraction efficiency but it was around 15%. Do you have any idea how can we increase diffraction efficiency??

one more question : I would like to use SLM as a multi beam generation as a beam splitter. could you explain me please how which order I use to get higher diffraction efficiency?

Hi Kipp, I didn't fully get how to get only amplitude modulation out of phase SLM. Can you provide equations?

Thanks.

Hi Kipp!

I would like to get a collimated line using an SLM. For which I am focusing a collimated circular beam using a cylindrical lens on to an SLM. If the SLM is off the line would diverge after reflection from SLM. By adding proper phase on the SLM can I make the line that hits on the SLM to stay as a collimated line ?

Thanks

Jitendra

Yes, you can do that with a phase-only SLM. When the SLM is off it will act similar to a mirror (no spatially varying phase change). So if your beam is diverging before it hits the SLM it will continue to diverge after hitting the SLM. However there will be some diffraction into higher orders due to the pixels being less than 100% fill factor. When the SLM is on, you would need to write the correct phase pattern to offset the beam divergence. This would not work with super narrow beams as you will need several pixels across the beam in order to write w proper lens function.

Thanks Kipp! I tried to do it however it's extremely difficult to do it. But Suppose I continue illuminating the SLM with line and I give a random phase on the SLM which is same along the horizontal axis such that I create a line with different phases in y direction. Now I know what phase I have given to the SLM. However since it is being illuminated not by a plane beam instead a converging line (using a cylindrical lens). And then I use a 4 -f system to image SLM on to CCD. And on CCD what will be the phase I get? Will it be same as that I gave on the SLM or will it be affected by the Cylindrical lens? If so how can I determine the phase at the CCD.

Can you please give some suggestions help!

Jitendra

The phase you impart with the SLM is additive to whatever phase already exists in the beam, and whatever phase changes might occur after the SLM from lenses or other optical components.

Thanks Kipp!

So since I am placing a cylindrical lens in front of a plane beam the phase introduced at the line on the slm will be exp(i*2*pi*lamda*X.^2). ? Am I correct ?

Kipp Bauchert , you have mentioned before about SLM calibration. I.ve got a Meadowlark SLM 1920x1152 XY Phase Series and I am using a 1035 nm pulsed laser. Meadowlark does not provide a calibration at this wavelength, could you please give me some advice of how to do it myself?

Marius, please send a message to slmsupport at meadowlark dot com and someone will send you a document detailing the process we use for generating our calibration files.