Feidhlim T. O'Neill

Photopolymer holographic recording material

Summary Photopolymers are promising materials for use in holography. They have many advantages, such as ease of preparation, and are capable of efficiencies of up to 100%. A disadvantage of these materials is their inability to record high spatial frequency gratings when compared to other materials such as dichromated gelatin and silver halide photographic emulsion. Until recently, the drop off at high spatial frequencies of the material response was not predicted by any of the diffusion based models available. It has recently been proposed that this effect is due to polymer chains growing away from their initiation point and causing a smeared profile to be recorded. This is termed a non-local material response. Simple analytic expressions have been derived using this model and fits to experimental data have allowed values to be estimated for material parameters such as the diffusion coefficient of monomer, the ratio of polymerisation rate to diffusion rate and the distance that the polymer chains spread during holographic recording. The model predicts that the spatial frequency response might be improved by decreasing the mean polymer chain lengths and/or by increasing the mobility of the molecules used in the material. The experimental work carried out to investigate these predictions is reported here. This work involved (a) the changing of the molecular weights of chemical components within the material (dyes and binders) and (b) the addition of a chemical retarder in order to shorten the polymer chains, thereby decreasing the extent of the non-local effect. Although no significant improvement in spatial frequency response was observed the model appears to offer an improved understanding of the operation of the material.

Photoresist reflow method of microlens production Part I: Background and experiments

Summary We present a two part study of melted microlens arrays. This first part concentrates on the production and measurement of microlens arrays while the second part examines attempts to model the microlens profiles. In this paper we first review some of the fabrication techniques used over the past twenty years to produce lens arrays. Some applications of microlens arrays are then discussed. Particular emphasis is placed on the photoresist reflow method of microlens production that was suggested by Popovic et al., as this was the method used to produce the microlens examined in this study. Lenses produced using this method can have large deviations from the spherical case, i.e. the profile that would be expected from a simple minimisation of the surface energy. These deviations have not been explained to date in the literature, however a number of possible causes for this deviation are given in this paper. Therefore the fundamental questions we wish to explore here are: (1) Why physically do dips occur? and (2) Can the resulting surface profile be predicted? Any model developed to quantitatively estimate the optical effects of surface shape will depend on the physical assumptions made regarding the surface formation mechanism. However as we shall indicate at this point only an informed guess regarding the relative importance of a number of possible mechanisms can be made.

Temporal analysis of grating formation in photopolymer using the nonlocal polymerization-driven diffusion model

The nonlocal polymerization-driven diffusion model (NPDD) has been shown to predict high spatial frequency cut-off in photopolymers and to accurately predict higher order grating components. We propose an extension to the NPDD model to account for the temporal response associated with polymer chain growth. An exponential response function is proposed to describe transient effects during the polymerization process. The extended model is then solved using a finite element technique and the nature of grating evolution examined in the case when illumination is stopped prior to the saturation of the grating recording process. Based on independently determined refractive index measurements we determine the temporal evolution of the refractive index modulation and the resulting diffraction efficiency using rigorous coupled wave theory. Material parameters are then extracted based on fits to experimental data for nonlinear and both ideal and non-ideal kinetic models.

Holographic photopolymer materials: nonlocal polymerization-driven diffusion under nonideal kinetic conditions

The kinetics of photosensitive polymer holographic recording materials are examined assuming a material that exhibits nonideal kinetic behavior. Previously, a linear relationship between monomer concentration and polymerization was assumed when deriving the nonlocal polymer-driven diffusion (NPDD) model. This is consistent with ideal kinetic conditions in which chain termination is governed by a bimolecular process. However, these models have been reported to disagree with experimental results. In a limiting case of nonideal kinetics it is assumed that primary termination is dominant. In this case the NPDD model must be modified to incorporate a quadratic relationship between the monomer concentration and the polymerization rate. By use of a multiharmonic expansion method of solution the predictions of ideal (bimolecular or linear) and nonideal (primary or quadratic) kinetic models are compared. By using these models we carried out numerical fits to experimental growth curves of gratings recorded in an acrylamide-based cross-linked photopolymer system. Superior fits are achieved by use of the primary termination model. Physical parameters such as the diffusion constant are extracted and compared with results previously reported in the literature.

Comparison of holographic photopolymer materials by use of analytic nonlocal diffusion models

The one-dimensional diffusion equation governing holographic grating formation in photopolymers, which includes both nonlocal material response and generalized dependence of the rate of polymerization on the illuminating intensity, has been previously solved under the two-harmonic expansion assumption. The resulting analytic expressions for the monomer and polymer concentrations have been derived and their ranges of validity tested in comparison with the more accurate numerical four-harmonic case. We used these analytic expressions to carry out a study of experimental results presented in the literature over a 30-year period. Automatic fitting of the data with these formulas allows material parameters, including the nonlocal chain-length variance sigma, to be estimated. In this way, (i) a quantitative comparison of different materials can be made, and (ii) a standard form of experimental result presentation is proposed to facilitate such a procedure.

Thickness variation of self-processing acrylamide-based photopolymer and reflection holography

There are many types of holographic recording material. The acrylamide-based recording material examined here has one significant advantage: it is self-processing. This simplifies the recording process and enables holographic interferometry to be carried out without the need for complex realignment procedures. However, the effect that the polymerization process has on the grating thickness must be examined. This question is fundamental to the materials use in holographic optical elements, as thickness variations affect the replay conditions of the pro- duced elements. This paper presents a study of this thickness variation and reports for the first time the production of reflection holographic grat- ings in this material.

Diffusion-based model of holographic grating formation in photopolymers : generalized non-local material responses

It has recently been shown by Sheridan and Lawrence (Sheridan J T and Lawrence J R 2000 J. Opt. SA A 17 1108-14) that, introducing a Gaussian non-local material response function into the one-dimensional diffusion equation governing holographic grating formation in photopolymers, both high-frequency and low-frequency cut-offs in the spatial frequency response of the materials can be deduced. In this paper generalized non-local responses are examined. These include a Chernov material response, and both the Chernov/Debye and Gaussian responses generalized to include a power-law response. The effects of these responses are examined for various material parameters, including the non-local variance, σ, the power-law degree, k, and the ratio of the rate of diffusion to the rate of polymerization, R. The resulting variations in monomer and polymer concentrations, the cross-sectional grating profiles and the spatial frequency responses predicted are presented and discussed. It is shown that in general, assuming an isotropic even, area-normalized response function, qualitatively acceptable growth curve and spatial frequency response behaviour are observed in all cases.

Temporal response and first order volume changes during grating formation in photopolymers

We examine the evolution of the refractive index modulation when recording gratings in an acrylamide based photopolymer. A nonlocal diffusion model is used to predict theoretically the grating evolution. The model has been developed to account for both nonlocal spatial and temporal effects in the medium, which can be attributed to polymer chain growth. Previously it was assumed that the temporal effect of chain growth could be neglected. However, temporal effects due to chain growth and monomer diffusion are shown to be significant, particularly over short recording periods where dark field amplification is observed. The diffusion model is solved using a finite-difference technique to predict the evolution of the monomer and polymer concentrations throughout grating recording. Using independently measured refractive index values for each component of the recording medium, the Lorentz-Lorenz relation is used to determine the corresponding refractive index modulation. The corresponding diffraction efficiency is then determined using rigorous coupled wave analysis. The diffraction efficiency curves are presented for gratings recorded using short exposure times, monitored in real time, both during and after recording. The effect of volume shrinkage of polymer on grating evolution is also examined. Both the nonlocal temporal response of the material and monomer diffusion are shown to influence refractive index modulation postexposure.

Photoresist reflow method of microlens production Part II: Analytic models

Summary In this paper attempts to model microlens surface profiles are discussed. The models used are analytic models. These models are examined for a range of different f numbers, f /#, and used to fit the experimental data discussed in the previous paper, Part I. A comparison of the models is made and the predicated aberrations are calculated. Theestimated aberrations are also compared to experimental results previously published in the literature.

Speckle photography : mixed domain fractional Fourier motion detection

A reflection-based optical implementation of two simultaneous scale-invariant fractional Fourier transforms (FRTs) is used to develop a novel compact speckle photographic system. The system allows the independent determination of both surface tilting and in-plane translational motion from two sequential mixed domain images captured using a single camera.