Workshop on Engineering Application in Astronomy.
Experiment 3: Optical Metrology with Hartmann Mask
Introduction: The Hartmann test was invented more than a century ago for optical metrology.. It
has been the predecessor to methods in Adaptive Optics, Opthalmology and Laser Characterization.
Figure 1: Hartmann wavefront sensor operation
As shown in Figure 1, the Hartmann mask consists of an array of 4 ⇥ 4 small apertures (holes) on a
metallic sheet. A plane wavefront creates an array of images (on a screen/detector) similar to that of the
location of the apertures on the Hartmann mask. Any aberrations in the wavefront will deflect the images
on the detector/screen. The deflection of the images in the x/y-direction will depend on the local slope of
the incoming wavefront. The information from the deflection of the images from their original location is
used to create the overall shape of the wavefront.
Figure 2: Schematic of the Hartmann Test
Experiment: The schematic of the experiment is shown in Figure 2 (lengths are not to scale). A
collimated beam is extracted from a white light source, which is incident on the Hartmann mask. The
image of the apertures is caught on a translucent screen. A webcam is used to record the position of the
images on the screen. Any optical device to be tested is placed between the collimator and the Hartmann
screen (see DUT, Device Under Test, in Figure 2).
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Procedure: The procedure consists of running a series of MATLAB programs (provided on a laptop
during the experiment) in the following order:
1. Image verification: The program, webcam recordingvideo.m, provides a live feed of the image of the
screen. The webcam can be adjusted for getting the most optimal image, using this program.
2. Reference calibration: The program, thresh calibrate fastpeakfind.m, is run to extract the position
of the reference images on the screen (without the presence of any DUT). The program uses a 2D
gaussian correlation algorithm to detect the centroids of the spots on the screen. It consists of the
following tasks:
• Input the crop parameters (maximum and minimum x and y coordinates) to the program to
just include the 4 ⇥ 4 spots in the frame.
• Ensure that there is a red cross mark on the ’peak detection’ image, and that the program reads
’peak detection looks fine’.
• If the program reports that the ’peak detection is not optimal’, change the gaussian threshold
values in the program till the program reports that ’peak detection looks fine’.
3. Aberration measurement: The program, sh movie.m, is used to compute the wavefront shape at the
screen in real-time, from the position of the spots. The program also outputs the ’peak-to-valley’
wavefront value (in metres).
Devices Under Test (DUTs): After the above calibration procedure is completed, optical parameters
of two devices will be extracted from the ’peak-to-valley’ wavefront value at the screen (computed by
sh movie.m). The two DUTs are:
Figure 3: Hartmann test setup for measuring the radius of curvature of a double convex lens.
1. Double-convex lens: Figure 3 shows the computations associated with a double-convex lens used as
the DUT. Let be the ’peak-to-valley’ wavefront value at the screen, due to the double-convex lens
h2
placed at a distance of L from the screen. We can derive the relation = 2R
from the inset image
in Figure 3, where:
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• h = 16 mm is the ’half-height’ of the Hartmann screen
• R is the distance from the screen to the centre of curvature of the lens.
The total radius of curvature of the lens is the sum of R
computed.
and L, which is to be
i
E
µ 15
Figure 4: Hartmann test setup for measuring the angle of a Fresnel biprism.
Not certain!
a
2. Fresnel Biprism: They are very thin prisms (0.5 degree) used to determine the wavelength of
monochromatic light, thickness of transparent sheets etc. through interference patterns. Figure 3
shows the method of determination of the prism angle from the ’peak-to-valley’ wavefront value at the screen, .
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