Image Processing Reference
In-Depth Information
Chapter 3
Wavefront Sensing
3.1 Introduction
Detecting the effects of the atmosphere on a wavefront of light requires an instru-
ment that both senses and measures variations in the phase or optical path length
differences of the optical waves. Electronic imagers, film cameras, and human eyes
all record the intensity of light falling on them, so phase variations must be trans-
formed into intensity changes to be recorded. A wavefront sensor, then, is a tool for
measuring differences in the optical path length over a wavefront by transforming
the differences into intensity variations that can be recorded.
Wavefront sensors are divided into two classes, direct and indirect (Geary
1995). Direct wavefront sensors measure the phase variation of the aberration in the
wavefront. Two members of this class of sensor are the radial shearing and point
diffraction interferometers. Indirect wavefront sensors measure the local tilt in the
wavefront, or the differential wavefront. Examples of differential wavefront sen-
sors are knife-edge tests, Shack-Hartmann sensors, and Shearing interferometers.
This chapter explores wavefront sensors from a general perspective and then
focuses on detecting the lowest-order modes important to image stabilization and
beam steering. Wavefront sensors provide the first step in compensating for the ab-
errations present in the wavefront, i.e., detection of the aberrations.
3.2 Transforming Optical-Path-Length Differences to Intensity
Variations
By definition, a wavefront is a surface of constant phase, even if the wavefront is
aberrated. The aberrations in a wavefront are identified when the wavefront is com-
pared to some reference wavefront as shown in Fig. 3.1. The difference between the
two wavefronts is expressed as a difference in phase or optical path length.
Thus, a wavefront sensor takes an aberrated wavefront in and provides a mea-
sure or representation of the phase variation. This will be our working definition for
a wavefront sensor.
If the difference between the aberrated wavefront and the reference wavefront
is pure tilt, the effect in the focal plane is a displacement in the point of focus. Thus,
the tilt in a wavefront entering a lens focuses at a position displaced from the optical
axis of the lens. This is a straightforward example of how a lens can be used to
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