Delay and sum beamformed acoustic-resolution photoacoustic images are limited in resolution by the wavelength of the received acoustic signal. We seek to improve on this resolution in the case when the received signal is known to be generated by only a few absorbers. When the absorbers to be imaged are known a priori to be sparse then the reconstruction problem can be stated as an optimization problem aiming to minimize the residual between model predictions and measured channel data and also an L1-norm-based metric of sparsity. In brief, the strategy aims to express experimentally observed curved wavefronts in channel data as a super-position of simulated point-spread functions with a constraint on sparsity. The approach is similar in spirit to recent super-resolution contrast ultrasound approaches but uses an L1-norm minimization strategy. We have applied this optimization strategy to photoacoustic beamforming in both simulation and experiment. Simulation was conducted using Field II, and an experimental measure of resolving power was obtained by imaging the cross section of two wires at successively smaller separations. Experimental channel data was acquired using a 21-MHz Visualsonics array transducers with a Verasonics Vantage ultrasound platform for data acquisition. Simulations indicate potential to beat the ultrasound diffraction limit by a factor of four or more while current experiments achieve a factor of two resolution improvement. A possible application of this approach is for providing increased resolution images of the microvasculature surrounding cancerous tumors. Ongoing work aims to investigate in vivo performance of the proposed sparsity-constrained super-resolution approach.
Micromachined tunable Fabry-Perot interferometers based on compound semiconductors have earlier been proposed for fiber optic communications employing wavelength division multiplexing (WDM) for wavelengths around 1.55 µm. The cavity length in micromachined interferometers is varied by displacing one of the two distributed Bragg reflector (DBR) mirrors by electrostatic actuation of supporting beams. The filter's optical response for varying cavity lengths is simulated by a transfer matrix method, and the optical tuning efficiency of the filter is 0.53. We investigate three conventional filter designs using the finite element method (FEM) and compare it with a new proposed filter design. Using a mathematical model, deflection is analytically calculated and compared with finite element analysis results. Due to the way in which the mirror is integrated with a suspending framework of beams, bending within the mirror during actuation cannot be averted. The filter's optical performance demands that the mirror remain so flat that the maximum bending deflection is 1 nm for the mirror of given dimensions. Using a criterion based on mechanical and optical considerations, the dimensions of the beams suspending the mirror are optimized for each filter design under investigation. Combining the optical and mechanical simulations by FEM, wavelength tuning characteristics for each filter design are determined.