# Results

Table 1 shows the measured angles of diffraction and relative intensities for selected orders at normal incidence. The angles of diffraction are consistent with the predictions made using the grating equation.

Table 1: Diffraction angles at normal incidence
Diffraction
order
Observed
angle (deg.)
Theoretical
angle (deg.)
5th 19.3 19.1
6th 23.3 23.1
7th 27.3 27.3

Focal points were found at approximately 31 cm and 15 cm, which is consistent with those of a Fresnel zone plate.

Fig. 8 shows relative intensities of diffraction orders in a single plane with the blaze condition set for 9th order diffraction. The concentration of energy into the 9th order is consistent with predictions.

Fig. 9 shows the image captured on the camera in the focal plane. It represents the point spread function (PSF) of the DMD. The salient feature of the image is the vertical elongation, which is an indication of an acute astigmatism in the wavefront. Ideally, the light would be perfectly focused to a point in the focal plane, which would appear as a single pixel.

This astigmatism is due to an idiosyncrasy of the experimental set up. When viewed off axis, the cross section of the circular aperture of the Fresnel zone plate becomes an oval, resulting in measurable wavefront aberrations. This can be compensated for by adding the opposite aberrations to the zone plate pattern. The difference is a very slight diagonal stretch such that the rings would appear as circles when viewed at an angle.

Fig. 10 shows the PSF with the astigmatism correction, which decreased the spot size by roughly a factor of ten. The significance of this is that it demonstrates the ability of the DMD to accurately correct wavefront aberrations.

However, even the PSF with the astigmatism correction shows signs of further aberrations. One source of these is irregularities on the surface of the micromirror array itself. Fig. 11 shows an interferogram that represents a contour map of the phase front reflected by the DMD with all mirrors flat. It shows us that the DMD surface is shaped more or less like a potato chip, which would contribute to aberrations in the wavefront.

By putting the opposite wavefront into the interferogram, the surface aberrations of the DMD can be compensated for. Fig. 12 shows the corrected PSF, which is approximately 120 microns. This represents a spot size that is about 2.4 times the diffraction limit as given by the Rayleigh criterion, which demonstrates the ability of the DMD to correct for specific wavefront aberrations.