Fig. 1. (a) The conventional usage of two reflective elements for AO versus (b) the cascaded configuration of two refractive DPPs. DM: deformable mirror.

Fig. 2. (a) Schematics of the employed DPPs and their proposed cascaded configuration. DPP1 has 25 keystone-patterned electrodes that are distributed within an area of 12 mm in diameter, and DPP2 has 37 hexagonally patterned electrodes that can be circumscribed inside a circle of 12 mm in diameter. (b) Top and side views of the fabricated DPPs. (c) Stacked DPPs in their 60-mm cage system compatible packaging and electrical interfacing.

Fig. 3. Open-loop control method for simultaneous control of cascaded DPPs. (a) Control flowchart and (b) visualization of different steps of replicating a target wavefront.

Fig. 4. Experimental evaluation of the introduced open-loop control for replicating two example wavefronts using DPP1 and DPP2. A target wavefront is chosen and the control signals of the DPP1 are calculated. The keystone patterns on each plot show the voltage distribution of the DPP1. These control signals are used to estimate the DPP1 response by its response model. The two wavefront profiles on each plot compare the estimated response from experimental measurements. Bar plots compare the Zernike decomposition of the target and reproduced wavefronts at each step of the control algorithm depicted in Fig. 3(a). Interferometric measurements are performed using a HeNe laser (λ=632nm).

Fig. 5. Experimental results for replicating up to the sixth radial order of Zernike modes. (a) Comparing the maximum achievable mode amplitude and their corresponding purity [see Eq. (6)] using DPP1 and DPP2 individually (depicted by green squares and blue triangles, respectively), and simultaneously with the cascaded configuration and the proposed control method (red circles). (b) Overview of the wavefront profiles of the replicated Zernike modes using the cascaded DPPs. The top-left figure shows the overlay of DPP1 and DPP2 electrode patterns. Interferometric measurements are performed using a HeNe laser (λ=632nm).

Fig. 6. (a) Schematic layout of the developed AO microscope. P, pupil plane; O, object; OL, objective lens; EF, emission filter; and I, image. (b) Detailed view of the ray-tracing simulation model at the location of cascaded DPPs each having a 7-mm offset from the conjugated pupil plane. Simulation results depicting the amplitudes of the Zernike modes with respect to field positions for (c) the ideal case of having both DPPs directly at the pupil plane, (d) only DPP1 actuated while being positioned 7 mm behind the pupil plane, (e) only DPP2 actuated while being positioned 7 mm in front of the pupil plane, and (f) DPP1 and DPP2 actuated simultaneously at their offset-position. (g) Overview of the fully refractive AO microscope with the integrated cascaded DPPs.

Fig. 7. Imaging fluorescent micro-beads (Ø=1μm) behind an aberrating phase plate that mimics specimen-induced aberrations while deep tissue imaging. (a) Aberrated frames, corrected frames using (b) a single DPP and (c) the cascaded configuration, (d) quality score of the obtained frames after each iteration of the aberration estimation algorithm, and (e) the estimated wavefront error by executing the sensorless aberration estimation algorithm using stacked DPPs. Length of the scale bars is 20μm.

Table 1. Parameters of the sensorless aberration estimation algorithm employed for the experiments presented in this paper. M1 and M2 depict the minimum and maximum of the normalized spatial frequencies, respectively, to be used for calculation of the MF using Eq. (7).