Characterization of multiple beams generated via phase modulation
Maria Eloisa M. Ventura1*, Giovanni A. Tapang1
1National Institute of Physics, University of the Philippines, Diliman, Quezon City, Philippines
* presenting author:Maria Eloisa Ventura, email:mventura@nip.upd.edu.ph
We describe the loss of resolution arising from dividing the source aperture to generate multiple independently-controlled beams. The projection of multiple spots onto a transverse plane along the optical axis is useful in optical manipulation [1] and neurophotonics [2]. Rodrigo et al. [1] generated multiple spots to trap several particles whose motion can be controlled by translating the generated beams using a spatial light modulator (SLM). An SLM, which can modulate the phase of incident light according to an input pattern, has also been used to generate 3D light patterns to probe neuronal functions [2].

We explore the generation of multiple patterns on a single plane by two approaches: (1) aperture division [1, 3]; and (2) phase addition [3]. We employ the Gerchberg-Saxton (GS) algorithm to generate a target pattern using an SLM whose aperture is illuminated by a monochromatic plane wave [3]. The GS algorithm is an iterative method that determines the phase required to produce a desired intensity distribution with a constraint in the aperture.

In the aperture division method, the aperture of the SLM is divided into smaller apertures, each of which is used to generate a target pattern. The constraint to generate a pattern is assigned only to a particular subregion in the aperture. Changing the constraint in the SLM for each subregion allows for independent control of each pattern assigned to that sub-aperture. To get the effective aperture that will reconstruct the multiple-spot pattern, we added all the phase output from each GS algorithm routine, masked with its corresponding aperture slice. In this work, we characterize the loss of resolution and the image quality of the beams due to the subdivision of the SLM’s aperture.

We also implement the field phase addition method for independent control of the beams by means of phase modulation described in Ref. [3]. This method performs the GS algorithm for each of the target beam with the full original aperture as a constraint. The effective pupil function will then be the aperture with a phase equal to the sum of the phase outputs for all the beams.

We used an aperture with a size of 512 x 512 pixels. The target to be generated is an Airy pattern whose full width at half of maximum intensity is 86 pixels. We consider, a large circular aperture with 512-pixel diameter is divided into slices with equal angles as well as a 512 x 512 pixels square aperture is divided into smaller squares. The number of divisions corresponds to the number of Airy patterns to be reconstructed.

An Airy spot was used as the target intensity pattern in the GS algorithm for a corresponding slice of the SLM aperture. To compare the quality of the reconstructed Airy patterns, the full width at half maximum intensity for each of the generated spots were measured. The Linfoot’s criteria of merit [4] for each of the spots compared to the target Airy pattern were also calculated. We then took the ratio of the full width at half maximum (FWHM) of the resulting spot sizes with the analytic Airy spot size for the whole aperture.

We found that although the FWHM can be reproduced fairly regularly over increasing number of apertures, the standard deviation of the generated FWHM of the method of adding fields is smaller by a factor of 2.63 when compared to that of the subdivided SLM aperture. This factor is more apparent when considering a square aperture where the standard deviation of the Airy spots generated by the field addition method is 12.53 smaller than aperture division. The fidelity (F), structural content (C) and correlation quality (Q) is larger and closer to unity for the method of adding fields when compared with the aperture division method for both the circular and square configurations.

Simply dividing the aperture reduces the available spatial frequencies that reconstructs the target function. Although the target FWHM can be reached through the GS algorithm, it is at the expense of the image quality. The correlation quality Q is a measure of the alignment of the peaks of the compared signals and its low value for the aperture division method (average = 0.36) reflects this trade off. The calculated phase from the GS algorithm is limited both by the object support and the image domain constraints. The GS algorithm can only change the phase to within the optical system’s space-bandwidth product [5].

We have demonstrated that the field addition method is not affected by this limitation since we are using the whole aperture to generate the patterns. The resulting pattern is more regular and gives a better approximation to the analytic Airy spot. Since the phase for each target pattern can be calculated separately, one can use this method to simultaneously control different targets. The limitation in generating more points would be on the input power. This method is also computationally faster for the same number of points when compared to aperture division by a factor of at least N, where N is the number of points generated.

* MEM Ventura is a PhD student at the National Institute of Physics

References:
1. R. L. Eriksen, V. R. Daria, P. J. Rodrigo, and J. Glückstad, “Computer- controlled orientation of multiple optically-trapped microscopic particles,” Microelectron. Eng. 67-68, 872-878 (2003).
2. M. A. Go, C. Stricker, S. Redman, H. A. Bachor, and V. R. Daria, "3-D Light Patterns for Spine-Targeted Probing of Neuronal Function," Optics & Photonics News 24(12), 33-33 (2013)
3. P. L. Hilario, M. J. Villangca, and G. Tapang, "Independent light fields generated using a phase-only spatial light modulator," Opt. Lett. 39, 2036-2039 (2014)
4. G. Tapang, and C. Saloma, “Behavior of the point-spread function in photon-limited confocal microscopy,” Applied optics 41(8), 1534–1540 (2002).
5. G. Bautista, M. J. Romero, G. Tapang and V. Daria, “Parallel two-photon photopolymerization of microgear paterns”, Optics Communications 282, 3746 - 3750 (2009)


Keywords: Fourier Optics, point spread function engineering, spatial light modulator