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Wavefront sensing of light beams

Wavefront of a light beam can be defined as the surface formed by the loci of all the points that are in the same phase or are at an equal optical path length from the source. If a coherent light beam having a plane wavefront passes through a certain medium or reflects from a certain surface, its wavefront gets modified according to the characteristic of the transmitting medium or the reflecting surface as shown in figure 1. As a result, the shape of the plane wavefront gets distorted from that of the ideal shape. Such distortions in the shape of the wavefront from that of the ideal wavefront are termed as wavefront aberrations. The wavefront aberrations are sometimes a nuisance leading to loss of information carried by the original wavefront whereas sometimes it may be helpful in studying the characteristic of the transmitting medium or the reflecting surface. Thus, in both cases, it is important to measure the wavefront aberrations introduced by the transmitting medium or the reflecting surface. The device used to measure the wavefront aberrations is known as wavefront sensor. Wavefront sensors are broadly classified as zonal wavefront sensors and modal wavefront sensors. The Shack-Hartmann wavefront sensor is a common example of zonal wavefront sensors whereas the bias beam based modal wavefront sensor is a common example of modal wavefront sensors.

Figure 1: Representation of wavefront aberration introduced by a transmitting medium and a reflecting surface.

The zonal wavefront sensor divides the incident wavefront into a number of zones or sub-apertures and the slope of each zone is measured individually. The slope information of all the zones is combined together to reconstruct the shape of the whole wavefront. The amount of aberration present in the incident beam can then be estimated using suitable mathematical algorithms. In the case of a Shack-Hartmann wavefront sensor (shown in figure 2), the wavefront is divided into small zones with the help of a two-dimensional array of tiny identical lenses. When a collimated beam with a plane wavefront is incident on the lens array, it gives rise to a two-dimensional array of focal spots at the common focal plane of all the lenses. When a distorted wavefront is incident on the lens array, the focal spots get shifted from the nominal position depending on the amount of slope of the individual zones. The slope of each zone is measured from the amount of shift of the focal spots of the respective lens. On the other hand, a modal wavefront sensor (shown in figure 3) realizes the wavefront as a linear combination of a set of orthogonal aberration modes. Here the incident beam is divided into two beams with identical copies of the incident wavefront and equal intensities. The two beams are then allowed to pass through two different phase plates and are later focussed to two point detectors. A fixed amount of a certain aberration (bias aberration) is added to one of the beams (called the positive bias beam) while the same is subtracted from the other (called the negative bias beam). If the bias aberration is present in the incident beam, the amount of the aberration in one of the beam increases leading to a decrease in intensity at the corresponding detector whereas the aberration of the other beam decreases leading to an increase in intensity at the corresponding detector. The difference in intensities of the two detectors gives a measure of the amount of the bias aberration present in the incident beam.

Figure 2: Principle of Shack-Hartmann wavefront sensor.

Figure 3: Principle of bias beam based modal wavefront sensor.

Both the two types of wavefront sensors can be easily implemented using binary holograms (refer to Programmable Diffractive Optics) as shown in figure 4. In the case of the zonal wavefront sensor (shown in figure 4(i)), the array of lenses can be replaced by an array of binary diffraction gratings (or binary holograms) that gives rise to an array of +1 diffraction orders at the focal plane of a lens placed just behind the grating array. While in the case of the modal wavefront sensor (shown in figure 4(ii)) the beam splitter and the phase plates are replaced by a binary hologram that gives rise to +1 and -1 diffracted beams. This +1 and -1 diffracted beams act as the positive and the negative bias beams respectively.

Figure 4: (i) Principle of grating array based zonal wavefront sensor (For more details see, Optics Letters: 35 202-204 (2010).) and (ii) holographic modal wavefront sensor (For more details on our relevant recent work see, JOSA-A: 36 741 (2019).)