THORLABS WFS20-14AR, Operation Manual

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Wavefront Sensor
8.6 Example Zernike Calculations
Example Tilt:
Q: How can the linear wavefront tilt in x direction be derived from a measured Zernike coeffi-
cient of Z3 = 0.1 µm at a pupil diameter of 4 mm?
A: With a normalization factor of 2 the wavefront shape
WF(x)
in Cartesian coordinates is:
WF(x) = 0.1 µm*2*x
Since the normalized x coordinate ranges from -1 to +1 within the unit circle, the maximum
wavefront deviation is therefore -0.2 µm at x = -1 and 0.2 µm at x = 1.
That is, we have a total tilt of 0.4 µm across the entire physical pupil diameter of 4 mm which
gives a tilt angle of
arctan
(0.4 µm / 4 mm) = 0.1 mrad = 0.0057 deg.
Example Defocus:
Q1 : What peak-to-valley (PV) deformation corresponds to a Defocus term of Z5 = -1 µm?
A1 : As the pure mathematical defocus formula (2r
2
- 1) describes a concave wavefront, the
wavefront shape
WF(
r
)
in polar coordinates is:
WF(
r r
2-1)
Since the normalized radial coordinate
r
ranges from 0 to 1 and the spherical shape achieves
its minimum and maximum wavefront deviation at these points, the PV value is just the differ-
ence
PV=WF(
r
=0) – WF(
r
This PV result is independent of the physical pupil diameter because it just describes the wave-
front deviation in z direction.
Q2 : What Radius of Curvature (RoC) is related to this spherical wavefront when measured at
a pupil diameter of d = 3 mm?
A2 : To convert the PV value into a RoC result, a standard mathematimatical circle function is
used. In literature [2] under ‘Sagitta’ the following formula is given:
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