DMD optical Setup: Diffraction-limited resolution

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Discussion Overview

The discussion revolves around calculating the diffraction-limited resolution for an optical setup involving a DMD (Digital Micromirror Device) and various lenses. Participants explore the implications of numerical aperture (NA), lens configuration, and the relationship between diffraction limits and pixel size.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant proposes that the diffraction-limited resolution can be calculated using the Rayleigh criterion, suggesting a value of approximately 4.6 µm based on the given parameters.
  • Another participant argues that the diffraction limitation of the illumination beam is independent of the DMD pixel size, stating that the resolution is defined by the size of the field aperture located between lenses 2 and 3.
  • A later reply clarifies that there is no field aperture between lenses 2 and 3, indicating that the diffraction orders of the DMD are recombined using a 4f-setup.
  • Further, it is suggested that Lens 2 acts like a microscope observing DMD pixels, with its resolution dependent on its numerical aperture in the object space, and that the absence of an aperture stop could lead to varying resolution across the DMD field.
  • Another participant raises the issue of projection angle, suggesting that the projected field is tilted and proposing that illumination could be done at an angle with optics working orthogonally to the DMD.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between diffraction-limited resolution and DMD pixel size, with no consensus reached on the correct interpretation of the optical setup's limitations.

Contextual Notes

Participants note the importance of defining an aperture stop for Lens 2 and the implications of projection angles on the setup's performance. The discussion highlights the complexity of the optical configuration and the potential variability in resolution across the DMD field.

Peter_44332
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Hi! I'd like to calculate the diffraction-limited resolution for the following optical setup:

1755455429074.webp

  • 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!
 
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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.
 
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.
 
DMD setup resolution.webp

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?
 
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