Are you using the SLM to control just amplitude? If so and assuming that the 4f system is setup correctly, the light at the output should be collimated. If your using the SLM to control amplitude and phase, then the light at the output of the 4f system won't necessarily be collimated. Generally speaking, it is very easy to check if CW laser light is collimated using a shearing interferometer. Thorlabs sells them for fairly cheap: see https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=2970.

Hi, Milo, thanks very much for your kind answer. I may not have described my problem clearly. In fact, I want to precisely measure the lateral displacement of some beams during its propagation. In the experiment, the incident light beam before the SLM has been calibrated to be coaxial and with a low divergence angle. It will be no off-axis displacement during propagation before the SLM. While the modulated beam by the SLM modulation and 4f system will off-axis during propagation. For example, I experimental generate a Laguerre-Gauss beam using an SLM and a 4f system. The generated LG beam behined the ouput plane of the 4f system will off-axis (a small lateral displacement) during propagation. I drew a sketch to better describe my problem. I initially think the optical paths in the 4f system are not perfectly coaxial causing the exit beam off-axis. I don't know if there is an efficient method to overcome this problem.

Thanks

I'm still confused: you're trying to remove the tilt, right? You should be able to do that with the SLM, especially if the tilt is small. Move the camera as far away from the second lens as possible and add tilt to the SLM until the beam is centered on camera's sensor.

Yes, I want to keep the light beam at a fixed position in the camera's sensor when I moving the camera (mounted on rail) away from the second lens. It is possible to achieve the above requirements by changing the blazed grating or tilting the SLM's screen. I'm going to try it.

Thank you very much!