Advanced Optics Lab – Spring 2012
Point Spread Function Engineering – Experiment
1. System setup
During this lab you will be using a programmable optical system to generate different point spread functions (PSF)
for joint optical-digital processing. The optical system layout is shown in Figure 1 and will be assembled before you
enter the lab.
The system operates as follows. The object is imaged by L1 into a 1:1, 4F imaging system implemented by L2 and
the reflective spatial light modulator (SLM) ( f L1  50mm , f L2  f L3  f  100mm ). The final output image is
recorded on the CCD camera. The SLM is placed in the Fourier plane of the 4F system and is used to implement
the phase profile that generates the desired Point Spread Function (PSF). Because no light is being absorbed, this
type of encoding (phase-only) is useful due to its higher efficiency. A color filter (not shown in the figure) is placed
in the imaging system with a peak at 585nm and FWHM of approximately 60nm.
Figure 1: Optical System Layout
2. Spatial Light Modulator
The spatial light modulator used in this experiment provides phase-only modulation of the incident field. It works
by applying a voltage across a liquid crystal layer in order to align the molecules such that the refractive index is
modulated for one polarization state.
The Boulder Nonlinear Systems (BNS) SLM allows the user to upload 8-bit (0-255) *.bmp formatted files and
display them on the spatial light modulator. This particular model is a 512x512 array of 15um pixels. The fill factor
is > 90%. Note that although the bitmap is 256 levels, this SLM will typically have only 50-100 resolvable phase
levels. The pixel values represent a phase shift from 0-2π.
Figure 2: (left) Boulder Nonlinear Systems spatial light modulator. (right) The liquid crystal within the spatial light
modulator is controlled by varying the applied voltage to the pixel electrodes.
3. Clear aperture imaging
To get used to the different parts of the imaging system and their functionality begin this lab by placing an object
(such as a crayon box) 10-20 cm away from L1. Adjust the position of the lens L1 such that part the object is in
focus. Lock the lens in place.
In this lab we will experiment with several pupil phase encodings that provide unique advantages over the clear,
circular aperture.
4. Extended depth of focus by wavefront coding
In this section you will create different cubic phase masks for extended depth of focus imaging. Use the analytical
form in equation (1) to create bitmaps with α=10, 20, 40, and 80 [x,y are normalized coordinates (-1 < x,y < 1)].
(1)
a.
What is the difference between these masks? What is the effect of different α values?
Figure 3: A cubic phase map (gray levels represent different phase values)
Save the masks in *.bmp format as discussed earlier and load them onto the lab computer that controls the SLM
and Point Gray camera in the C:\COSIUsr\ file folder. Start the SLM control software by double clicking on the Blink
software icon on the desktop. You can load the bitmap that you created by clicking on ‘Insert’ in the ‘Sequence’
portion of the window. Select your cubic phase mask and the *.lut file ‘. The *.lut file contains a list of proper
voltages to apply to the SLM backplane in order to control the phase. These are individually calibrated for each
SLM using an interferometer setup to correct for a flat phase front.
Now start the Point Gray camera software. This is the FlyCap program and can be found on the desktop.
In order to study the PSF of the optical system you will use a point source generated by a white light lamp and
spatial filtered by a pinhole. Place the point source around the object plane selected in 3. If you turn on the white
light source (the object to be imaged), you should see that the image is a Gaussian looking function. If you return
to the Blink software and turn the SLM power ‘On’, you should see this image distort to the PSF expected of the
cubic phase mask encoded exit pupil.
b.
Record the PSF for different axial positions of the point source to cover the whole range of PSF invariance
(save at least 5 images with their object respective location). Repeat for the different values of α.
c.
Replace the point source object with the crayon box found in the lab. Illuminate the object with the white light
source. Collect images of the object with and without the cubic phase encoded pupil. You can switch between
different phase masks with the SLM. What do you notice about the image with the clear circular aperture
versus the cubic phase aperture?
d.
Save the images you acquired with different phase masks. Restore the cubic-phase images to attain an
extended depth of focus by using Wiener deconvolution. You should be able to restore the images to look
similar to the best clear-aperture image but now extended beyond the traditional depth of field.
5. Ranging using a Rotating Point Spread Function (RPSF)
a.
Create a phase mask using the phase of the function f RPSF generated in the prelab. The size of the bitmap
should match the number of pixels on the spatial light modulator. The result should look like the mask shown
in Fig. 4. You will need to experiment and choose the appropriate scaling for f RPSF .
Figure 4: Phase of the RPSF
b.
Measure the PSF along the range of rotation of the PSF using a pinhole and the white light source. Record at
least 10 images in this range and take note of the distance from the lens L1. Plot the angle of rotation as a
function of distance from the lens L1. How would you calculate the angle of rotation? Does this plot agree with
what you would expect from theoretical calculations? Compare.
c.
Now you will find the range (axial distance) of an object placed within the range of rotation found in the last
section. Record images of a sharp bright object such as the tip of a pen. Find the location of the tip using the
calibration plot of section 3.c.