Hartmann-DIMM

The H-DIMM method for measuring the astronomical seeing is a modification of the ESO-DIMM. So all the theory mentioned until now, applies to both methods equally. In the H-DIMM the two images are produced by a simpple out of focus hartmann mask, with no prism. So here i will tell only for the influnce of the defocusing of the telescope, since for the calculation of the seeing value through the differential image motion, the same equations are used.

Elimination of the image separation prisms is possible because the depth of field of the sub-apertures is much larger than that of the parent optical system. For an aperture diameter $D$, wavelength $\lambda$ and focal length $f$, the depth of field is given by :

$$2\Delta Z=1.22\lambda\bigg(\frac{f}{D}\bigg)^2$$ (3.16)

Therefore, if the imaging CCD is displaced from best focus by an amount $<\Delta Z$ (either inside focus or outside focus), then the point spread function produced by each sub-aperture will be indistinguishable from perfectly focused subaperture images. However, the images produced by sub-apertures separated by a distance $d$ become well separated when :

$$\Delta z>1.22\lambda\bigg(\frac{f}{d}\bigg)^2$$ (3.17)

When the detector is located at a distance $Z$ from the focal plane of the imaging telescope, where $\Delta z<Z<\Delta Z$, all images of a star produced by subapertures separated by more than $d$ from each other will be well separated in the image plane, and will be in perfect focus. Under these circumstances, the differential image motion is easy to determine from the fluctuations in the centroids of each image from one exposure to the next.

An optimal ratio of image separation to diameter is achieved by locating the detector at $Z\approx\Delta Z$ from best focus.