EELE 482 Lab #5

Lab #5

Shack-Hartmann Wavefront Sensor

(1 week)

Contents:

1. Summary of Measurements 2

2. New Equipment and Background Information 2

3. Beam Characterization of the HeNe Laser 4

4. Maximum wavefront tilt 4

5. Spatially Filtered Beam 4

6. References 4

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1. Summary of Measurements

HeNe Laser Beam Characterization 1. Use the WFS to measure both beam radius w and wavefront radius R at several locations along the beam from the HeNe laser. Is the beam well described by the simple Gaussian beam model we have assumed? How do the WFS measurements compare to the chopper measurements made previously?

Characterization of WFS maximum sensible wavefront gradient 2. Tilt the wavefront sensor with respect to the HeNe beam while monitoring the measured wavefront tilt. Determine the angle beyond which which the data is no longer valid.

Investigation of wavefront quality after spatial filtering and collimation with various lenses 3. Use a single-mode fiber as a spatial filter. Characterize the beam emerging from the fiber for wavefront quality, and then measure the wavefront after collimation using a PCX lens and a doublet. Quantify the aberrations of these lenses.

2. New Equipment and Background Information

1. Shack-Hartmann Wavefront Sensor (WFS) The WFS uses an array of microlenses in front of a CMOS camera, with the camera sensor located at the back focal plane of the microlenses. Locally, the input beam will look like a portion of a plane wave across the small aperture of the microlens, and the beam will come to a focus on the camera with the center position of the focused spot determined by the local tilt of the wavefront. The concept is illustrated in the figure below (taken from the WFS manual).

With knowledge of the focal length of the microlens and the position of the focused spot, the local wavefront tilt is determined for each microlens. This tilt (wavefront spatial derivative) can be integrated to recover the overall shape of the wavefront. This sensing scheme is an alternative to interferometry for measuring wavefront shapes. It can work for both large and small wavefront tilts (scalable by changing the focal length of the microlenses), and does not suffer from the susceptibility to vibration of interferometers.

Because the camera is imaging many focused beamlets across the aperture, both wavefront tilt and intensity are measured (by the position and brightness of the measured spots, respectively). Our WFS therefore can be used for intensity profiling of the beam at the same time it is measuring wavefront shape.

Detailed information about use of the WFS is provided in the manual, which is available as a PDF file on the course webpage. The link is next to the link you followed to download this writeup.

2. Interpreting the Data from the WFS The WFS can output intensity and wavefront maps as raw numbers (W/m2 or m of wavefront sag, respectively). Perhaps more useful, however, are parameters that describe a best-fit curve to the measured data. For instance, the intensity profile can

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2 be fit to a Gaussian, with 2wx and 2wy determined as the 1/e intensity diameters measured in the x and y directions. The wavefront is fit to a sphere to determine the radius of curvature RoC. It is also fit to a family of orthogonal two-dimensional polynomials called the Zernike polynomials. Fitting an optical wavefront to a series of Zernike polynomials is the usual way to parameterize aberrations, especially in the laboratory (other expansions, like the Seidel terms, may be used in the theoretical analysis of axially symmetric systems).

Details about Zernike polynomials are beyond the scope of this lab, but for reference I am including this table from the WFS manual, showing the first 15 Zernike “modes” as both polynomials and as interferograms that would be observed in an interferometer for a wavefront corresponding to a pure Zernike mode.

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3. Beam Characterization of the HeNe Laser

From last lab we know that we can characterize a Gaussian beam by three parameters: the beam waist size wo, the location of the waist z and the wavelength of the beam . We know the wavelength of the beam for the HeNe laser is  = 632.8 nm. Determination of the two remaining parameters thus requires at least two measurements. In practice, a more accurate determination is made by measuring the beam at several locations and fitting the results. Using a chopper or a simple camera, we can measure the beam radius w at several z locations, and fit that to the hyperbolic expression for w(z). The Shack- Hartmann sensor can similarly measure beam diameter (assuming a Gaussian fit) based on the intensity distribution across the sensor. Alternatively, the beam wavefront radius of curvature R can be measured directly at several locations z, and this can be fit to the expression for R(z) to obtain the best-fit Rayleigh parameter. a) Use the WFS to measure both the beam spot size w and the wavefront radius R of the HeNe laser at 4 or 5 positions along the beam. You will need to attenuate the beam using crossed polarizers or neutral density filters so that you do not saturate the WFS camera. You may need to use one or two mirrors to fold the beam, in order to make measurements significantly distant from the laser endface. b) After lab: Fit your measurements to the theoretical expressions for the variation of w(z) and R(z) in order to predict wo and zo, as well as the location of the waist of the beam relative to the output face of the laser. Plot your data for both w(z) and R(z), along with your best fit theoretical curve. Do your results for w(z) agree with the results from the chopper measurements?

4. Maximum wavefront tilt

Rotate the WFS with respect to the beam, and watch the wavefront tilt grow on the display (in either “Wavefront” or “Zernike Coefficients” display modes). At what incidence angle does the display go out of range? This corresponds to the maximum wavefront tilt that can be measured using the WFS. To what minimum wavefront radius of curvature would this correspond, for a 4.5mm diameter beam?

5. Spatially Filtered Beam

(a) Measure the wavefront emerging from a single mode fiber. How far from the fiber must you be to have a wavefront radius of curvature that is within range of what the WFS can measure? (b) Use a PCX lens with f=50mm, mounted on a translation stage, to collimate the beam emerging from the fiber. Adjust the spacing to accurately collimate the beam, using the WFS to monitor wavefront radius of curvature (RoC, make this as large as possible) or defocus z5 (make this as small as possible). (c) Capture the Zernike spectrum for this configuration. Note the orientation of the lens with respect to the beam. (d) Now tilt the lens in the beam, 10 or 15 degrees (rotate it about the post axis), and re-adjust the axial position for maximum wavefront radius of curvature. What happens to the Zernike spectrum? What terms are affected by a lens tilt? (e) Fully reverse the lens (swap the plane and curved faces), readjust for best collimation, and save the resulting Zernike spectrum. What lens orientation makes the “best” plane wavefront, as measured by the WFS? Try to see some difference in z13, which is primary spherical aberration.

You will want to save the Zernike spectra, along with wavefront plots, to make a pretty lab report.

6. References

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