ERRATUM: Diffraction Effects in DMDs

I made a big mistake in the calculation of the DMD diffraction effects, it affects the following posts:

These will be edited shortly to reflect the corrections, as well as the paper A practical guide to digital micro-mirror devices (DMDs) for wavefront shaping (DOI, Arxiv) that will be retracted and resubmitted.

Long story short, the grating equation was wrong. It should not affect too much the results for low angles, but given the fact that the angles of each micro-mirror is already 12 degrees, it is not negligible at all.

The correct grating equation should be:

\[
  \text{sin}(2\theta_B-\alpha') + \text{sin}(\alpha')
  = 2 \,\text{sin}(\theta_B)  \,\text{cos}(\theta_B-\alpha')
  = p\frac{\sqrt{2}\lambda}{d} \, ,
\]

with the same notations as in the tutorial, so the blazed number then reads:

\[
  \mu =
  \left| 4 \frac{d}{\lambda\sqrt{2}}
  \left[
    \text{sin}(\theta')\text{cos}(\theta'-\alpha')
    \right]
  \mod{2} -1
  \right| \, .
\]

Big thanks to L. Malosse and @NiuYihan1999 for pointing out this error.



Created by admin on 15/01/2025

DMD