DMD optical Setup: Diffraction-limited resolution

[Peter_44332]

Hi! I'd like to calculate the diffraction-limited resolution for the following optical setup:

• Source: multimode fiber end, NA = 0.2 --> smallest NA, likely limiting?
• Wavelength: 1500 nm
• Lens 1 & 2: f = 50 mm & d = 25 mm
• Lens 3: f = 30 mm & d = 12.5 mm

Is it correct to assume that the diffraction-limited resolution (Rayleigh criterion) is δ = 0.61*λ/(NA) ≈ 4.6 µm?

Since my projected DMD pixel size is 8 µm, the setup would be sampling-limited rather than diffraction-limited, correct?


Thanks a lot for your help!

 

[Gleb1964]

Not correct. Diffraction limitation of the illumination beam is not connected to the DMD pixel size and it resolution. The size of illumination beam is only defining the size of illuminated area at DMD.
The resolution of the DMD projection is defined by the size of field aperture located at focus between lens 2 and 3. You haven't showed any aperture between lens 2 and 3 on the drawing, but the size of aperture at the beam focus is defining how wide diffraction angle is accepted from the DMD.

 

[Peter_44332]

Thanks for the reply! There is no field aperture positioned between lenses 2 and 3, the diffraction orders of the DMD are recombined with the 4f-setup.

 

[Gleb1964]

May be this picture helps.
Think about Lens 2 as a microscope looking at DMD pixels. Its resolution would be defined by the numerical aperture of Lens 2 in the object space (at DMD object), meaning how width angle of diffracted from DMD object would be accepted by lens 2 and consecutive optics.
If you have not defined any aperture stop for lens 2, it resolution may vary over DMD field as numerical aperture may vary. The best option I would aim telecentric condition for lens 2, setting the aperture stop at it focus (approximately where you have beam focused between lenses 2 and 3).
Another problem is that projection of DMD is done at some angle, meaning your projected field would be also tilted in the image space. Why not make illumination at angle and projection optics working ortogonal to the DMD?