Diffractive optical elements designed for highly precise far-field generation in the presence of artifacts typical for pixelated spatial light modulators.

Diffractive optical elements (DOEs) realized by spatial light modulators (SLMs) often have features that distinguish them from most conventional, static DOEs: strong coupling between phase and amplitude modulation, a modulation versus steering parameter characteristic that may not be precisely known (and may vary with, e.g., temperature), and deadspace effects and interpixel cross talk. For an optimal function of the DOE, e.g. as a multiple-beam splitter, the DOE design must account for these artifacts. We present an iterative design method in which the optimal setting of each SLM pixel is carefully chosen by considering the SLM artifacts and the design targets. For instance, the deadspace-interpixel effects are modeled by dividing the pixel to be optimized, and its nearest neighbors, into a number of subareas, each with its unique response and far-field contribution. Besides the customary intensity control, the design targets can also include phase control of the optical field in one or more of the beams in the beam splitter. We show how this can be used to cancel a strong unwanted zeroth-order beam, which results from using a slightly incorrect modulation characteristic for the SLM, by purposely sending a beam in the same direction but with the opposite phase. All the designs have been implemented on the 256 x 256 central pixels of a reflective liquid crystal on silicon SLM with a selected input polarization state and a direction of transmission axis of the output polarizer such that for the available different pixel settings a phase modulation of ~2pi rad could be obtained, accompanied by an intensity modulation depth as high as >95%.

Diffraction-based determination of the phase modulation for general spatial light modulators.

We describe a characterization method based on diffraction for obtaining the phase response of spatial light modulators (SLMs), which in general exhibit both amplitude and phase modulation. Compared with the conventional interferometer-based approach, the method is characterized by a simple setup that enables in situ measurements, allows for substantial mechanical vibration, and permits the use of a light source with a fairly low temporal coherence. The phase determination is possible even for a SLM with a full amplitude modulation depth, i.e., even if there are nulls in the amplitude transmission characteristic of the SLM. The method successfully determines phase modulation values in the full 2pi rad range with high accuracy. The experimental work includes comparisons with interferometer measurements as well as a SLM characterization with a light-emitting diode (LED).