1) The HS sensor measures the local slope (the gradient) of the wavefront. Using this kind of wavefront sensor you can in principle measure all the aberrations except the tip-tilt. The highest measurable aberration order depends on the number of lenses in the HS array. If used properly a commercial HS sensor can accurately measure a wavefront up to at least Z32 

2) When measuring a spherical wave you may need to remove the defocus term. This is usually done with a calibration procedure before collecting the real data. Some commercial HS sensors are equipped with software that will allow to do it automatically.

3,4) Depends largely on the optical system you are testing.

I recommend the book Optical Shop Testing, by Daniel Malacara.

1) The HS sensor measures the local slope (the gradient) of the wavefront. Using this kind of wavefront sensor you can in principle measure all the aberrations except the tip-tilt. The highest measurable aberration order depends on the number of lenses in the HS array. If used properly a commercial HS sensor can accurately measure a wavefront up to at least Z32 

2) When measuring a spherical wave you may need to remove the defocus term. This is usually done with a calibration procedure before collecting the real data. Some commercial HS sensors are equipped with software that will allow to do it automatically.

3,4) Depends largely on the optical system you are testing.

I recommend the book Optical Shop Testing, by Daniel Malacara.

Two other useful references are the "Adaptive optics engineering handbook" by Robert K. Tyson and "Introduction to wavefront sensors" by Joseph M. Geary.

Thank you Lacopo and Zoran for your response.

I have few additional questions:

Is it possible to measure chromatic aberrations with HS?

If I use light source and lens which aberrations can help me understand that lens located on the optical axis and not shifted?

Vladimir, HS sensor in most cases uses monochromatic sensors, so in order to measure chromatic aberrations, you will have to  measure separately  wave fronts at any spectral bands (say using color filters) and to analyze this offline. For instance different degrees of defocus across spectrum would correspond to longitudinal chromatic aberration.

The HS sensor is normally used with monochromatic light, and sequential measurements at different wavelengths would be performed to measure longitudinal chromatic aberration. However, I know of one paper, "RGB Shack–Hartmann wavefront sensor" by Jain and Schwiegerling, where the authors simultaneously measure aberrations in the eye at three visible wavelengths. See http://www.tandfonline.com/doi/pdf/10.1080/09500340701467728

You are limited to a slope of the spherical wave such that the Hartmann spots do not touch. This is of course true for any aberration. However, when the spots get very close, you will need to switch to Fourier analysis (http://www.opticsinfobase.org/josaa/abstract.cfm?id=79318). The software is available at http://physics.technion.ac.il/~eribak/exampl.m .

Light striking the lens parallel to the optical axis but offset from the center of the lens will have tilt and increased spherical aberration.  If the lens is tilted or the light strikes the lens at an angle to the principal plane, it will have tilt and coma.  Of course, these will be combined with the focus generated by the lens.  As noted above, Malacara is a great resource.

One of the great advantages of a Shack Hartmann using modern software is the ability to quickly and easily take a reference file. This allows for a Shack Hartmann user to isolate aberrations of the element under test from all the optics present when the reference file was taken. I don’t remember this point coming out strongly in Malacara. You might want to read the Dan Neal paper “Wavefront Sensors for control and process monitoring in optics manufacture.” If you have any trouble getting a copy send me an e-mail [email protected]

You could potentially analyze chromatic shift if you are able to take SH measurements using a number of monochromatic sources separately, and comparing them. You will be able to detect differences in wavefront shape (essentialy in radius of the final wavefront) in each of them.

If you compute the wavefront shapes in a number of different wavelengths you will be able to calculate both transversal (using Rayces equation) and axial chromatic aberration  easily.

Alternatively you could use a white-light source and some sort of filter wheel. Intensity here is not relevant while the beam is still detectable.

I have additional subquestion.

I performed some simple experiment with Thorlab's Shack-Hartman sensor. Some of it's  software outputs are 15 first Zernike coefficients and some image describing wavefront.

I performed simulation, to reconstruct wavefront, but since Zernike polynomials defined in the normalized circle of radius 1, then I reconstructed the wavefront inscribed in the circle and not inscribed into the square as in image from Thorlabs' software.

Which corrections I must perform to obtain exactly the same inscribed in the square image?

How influences of the fact that there are differences between representations on Zernike coefficients?

A set of Zernike coefficients has no meaning unless the Zernike aperture over which the analysis was completed is provided. I don’t know exactly how the Thorlabs software works, but once a set of Zernike coefficients are available points beyond the Zernike circle can be calculated. If the points are beyond the Zernike radius reported by the software, those points are extensions beyond the original data set and should be viewed as estimates. This is the case where the Zernike analysis circle is selected to fit completely inside the detector.

If the original Zernike fit was made using the furthest available data point, typically along the diagonal, then the original fix contains the full set of available data. There is a disadvantage to this method, too. If the Zernike radius was set by the diagonal of the data then the coefficients were calculated with holes in the data set where no centroid information exists. The four area of the circle where the arc of the circle extends beyond the detector’s rectangular area have no data, but are inside the Zernike analysis. This is the case where the Zernike analysis circle is made large enough to cover the detector area.

To analyze the physical size of your measurement you must scale by the aperture. Normalization is achieved by dividing the distance away from the center of analysis by the Zernike radius, which is often defined as the maximum distance from the center for which data exists. Multiply by the Zernike aperture to return to physical coordinates. In fact, determining the Zernike radius can be complicated. It is affected by the criteria for selecting the outer most area of interest. It is not necessarily just the coordinates of furthest from the analysis center centroid’s center of mass. Often, the size of the area of interest needs to be considered. Again sometimes averaging of data along edge points can be employed to calculate the Zernike radius. Of course if the Zernike radius is set by the user the existing data is used to calculate the best fit regardless of coverage, and the operator should review the residual fit error to ensure it is acceptable.

A zonal fit to the data does not rely on the Zernike fit process. It provides a map of the difference from your reference surface for all data points gathered. It is good for mapping, but does not provide a simple set of coefficients for later analysis.

1) SH sensor measures all aberrations that are within its resolution limit (the subaperture size). Aberrations beyond this limit create so called aliasing errors that need to be suppressed via focal plane masking (see, for instance Lisa A. Poyneer and Bruce Macintosh, "Spatially filtered wave-front sensor for high-order adaptive optics," J. Opt. Soc. Am. A 21, 810-819 (2004) ).

2) Generally SH sensor works in collimated beam, focus results in spread or shrink of the spot pattern on the camera. By itself it is not catastrophic given proper calibration but reduces dynamic range of the sensor. Adding a lens is good simply to "straighten" the wavefront, i.e. to make it flat. No other advantages.

3) Measuring aberrations and improving them are completely different tasks. Wavefront sensor only gives information about aberrations, quite accurately, but no more. You need some correction elements like deformable mirrors or just adjustable lenses to correct anything.

4) how well you correct aberrations depends entirely on the correction elements you have at disposal. A classical pair is SH sensor + deformable mirror, but I cannot go any further with my recommendations until I know more about your problem.

If Thorlab's SHWFS grabs wavefront based zernike mode reconstruction, I think that the main problem is the different zernike polynomials. There are three kinds of zernike polynomials: 1) OSA standard, it usually is used for retina adaptive optics; 2) Noll's zernike polynomial, it is often used in atmospheric turbulence simulation and correction; 3) fringe zernike polynomials: Zygo interferrometer uses it.   So, you should be clear which polynomial is used in Thorlab's SHWFS. Slopes calculations and reconstructions will make little differences for correct calculation process.

If Thorlab and you use zonal and mode reconstruction, respectively, the result will have a little difference. But the result is nearly the same especially for simple optical layout in lab.