Correcting depth aberrations with a DM improves both the peak intensities and the deconvolution of images taken below the cover slip by removing the depth aberration. This allows the use of fast space-invariant deconvolution algorithms instead of depth-dependent algorithms. This is significant because it improves both the signal-to-noise ratio and the resolution in biological imaging where photons are in short supply. Unfortunately, the performance does not yet achieve what is theoretically possible.
Although the correction of a bead in glycerol, , shows an impressive improvement in intensity due to the correction, the factor of 2 increase in signal is still less than the factor of 4 that should be possible based on the theoretical decrease in intensity predicted by the depth, NA and index of refraction mismatch. There are two important factors that contribute to this effect. The first is the effect of uncorrected aberrations from the sample and the optical path, which decrease the maximum intensity at the cover slip, but in a way that does not add linearly to the depth aberration. Thus only a fraction of the dispersed photons can be restored to the central peak. In closed loop AO systems, system aberrations are automatically compensated at each position (Wright et al., 2007
), but in an open-loop system this is not possible. The second factor is the inability of the mirror to precisely conform to the shape given by Eq. (1)
. The residual error of the mirror shape increases with depth (see ) so that as the imaging plane goes deeper and the possibility for improvement becomes greater, the improvement in peak intensities decreases. To address the first problem we must reduce the residual aberrations in the system as much as possible. The objective and tube lens will not be perfect (Juskaitis, 2007
), and the mirrors used in our system are also a potential source of aberrations. Most silver mirrors are specified to have a rms surface flatness of λ/10. According to the Marechal criterion (Hardy, 1998
), this will result in a Strehl ratio of roughly 0.6. Thus having a few mirrors in the system can be a significant source of aberration.
Similar to the residual aberrations in the optical train, sample-induced aberrations can affect the performance of the system in a nonlinear way and will affect the measured performance of the microscope in correcting depth aberrations. Scattering will also affect the ability of the microscope to recover the intensity lost since scattering will disperse the light in a random way so that it cannot be imaged.
Another important feature of three-dimensional wide-field microscopy is the out-of-focus light present in the three-dimensional PSF. As can be seen in and , the PSF of the system contains a weak grid of points outside the central peak due to the print-through. In confocal microscopy, only light in the central peak is accepted by the pinhole; therefore, the PSF should not be substantially altered although the intensity measured inside the pinhole is still less than ideal. In wide-field microscopy, the structure in the PSF can be visible in the image. Deconvolution is important for removing this structure, and the AIDA deconvolution package works well but could be further modified to explicitly address such features that arise in adaptive optics. Myopic deconvolution, allowing the PSF to vary under a harmonic constraint along with optimization of the reconstruction, is an option in AIDA, and it would be interesting to tailor the PSF constraint for the case of adaptive optics where the spatial frequency of the print-through is known, but its exact structure could be optimized to account for details of the PSF.
The ability to focus with the DM is very exciting for live imaging because it enables the acquisition of three-dimensional data rapidly without any movement or disturbance of the sample; DMs have typical response times of better than 200 Hz and modern cooled CCD cameras can capture 256 × 256 pixel images at faster than 60 fps. An active focus locking system has been implemented with adaptive optics by (Poland et al., 2008
) at over 200 Hz. Other motionless refocusing techniques are either not as fast (Tsai et al., 2007
) or cannot correct for the refractive index mismatch (Botcherby et al., 2007
). The optical system can be redesigned to use optical components with better surface quality, and there is also the possibility that the system could be calibrated to correct for the aberrations at every focus position.
There are many modifications to the microscope design that we discuss here that could improve correction of depth aberrations and extend the design to the correction of sample-induced aberrations. A DM with more actuators could be used to more faithfully approximate the depth correction term given by Eq. (1)
. One difficulty with this is that the dense-actuator devices typically can deform by at most a few wavelengths. To get around this difficulty, a microscope with two DMs in a ‘woofer-tweeter’ configuration could be designed using one large-throw actuator mirror and one dense-actuator low-throw mirror or liquid crystal device (Wright et al., 2006
). Another possibility is to design a DM specifically to focus with a shape given by Eq. (2)
. This DM could be designed to have only one or at most a few actuators to control the shape and would not have the problems with print-through from a grid of actuators, allowing it to be smaller and faster as well. Lastly, the ultimate goal of applying adaptive optics in microscopy is to correct all aberrations including those introduced by the refractive index variations of the sample itself. Thus, inserting additional DMs conjugate to several planes in the sample itself for correcting sample-induced variations over the field of view, as simulated theoretically (Kam et al., 2007
), is an important future goal.