Ray diagram of the depth aberration. (a) Diagrams the path length difference (n₂q-n₁q’) between an unrefracted ray (dashed line) from a point a depth d below the cover slip and a ray that is refracted at the interface (solid line). Compensating for this path length difference in the back pupil plane will correct the spherical aberration. (b) Shows the path length difference (n₂q-n₁q’) between a ray from a point just below the cover slip (dashed line) and a ray a depth d below the interface. Compensating for this path length difference in the back pupil plane will focus to a depth d and correct for spherical aberration.

Microscope layout. Grey represents the emission path. The blue striped beam is the excitation light and the red striped beam is the reference beam. See text for details.

(a) Cross-section of measured mirror shape (black circles) compared to the theory given by (blue line) for d = 5 µm with n₁ = 1.512, n₂ = 1.333, NA = 1.2. (b) Difference between measurement and theory from (a). (c) Measurement of wavefront error (blue circles, left axis) as a function of the shape applied to the DM. The corresponding Strehl ratio calculated using the Marechal equation is given by the red line on the right axis. The shape is given by with n₁ = 1.512, n₂ = 1.333, NA = 1.285 and depth given by the x-axis. 45 singular values were used in the singular value decomposition for these measurements.

PSF of the microscope measured at the cover slip. (a) PSF in focus scaled to maximum intensity. The images are 24 µm × 24 µm. (b) PSF in focus, logarithmic scale. A series of faint peaks are visible around the central PSF due to diffraction from the mirror print-through. (c) PSF 6 µm out of focus away from the cover slip. (d) PSF 6 | m out of focus towards the cover slip. (e) xz-cross-section of the PSF on a logarithmic scale. The image is 24 µm × 10 µm.

Back pupil plane calculated by phase retrieval from the three-dimensional image of a 200 nm bead at the cover slip. Amplitude (left) and phase scaled from −π/2 to π/2 radians (right). The DM print through is clearly visible. 20 of the actuators are at the edge of the mirror and therefore do not produce a print-through bump.

Images of a 200 nm bead 67 µm below the cover slip in a water/glycerol mixture with n = 1.42. (a) Uncorrected image of in-focus plane. (b) Corrected image of in-focus plane: same scale as (a). (c) and (d) are the same as (a) and (b), respectively, but on a logarithmic scale. (e) and (f) are cross-sections through the focal plane on a linear scale. The scale bars are 1 µm. (g) and (h) are line profiles through of the intensity through the centre of the bead along a lateral and the longitudinal axis, respectively. The dashed line is from the uncorrected image and the solid line is from the corrected image. (i) and (j) are simulations of the PSF. (i) corresponds to the uncorrected PSF 65 µm into a material with index 1.42 using a 1.2NA objective with a 1.512 refractive index immersion oil. (j) is a simulated PSF at the cover slip. The peak intensity for (j) is 3.75 times the peak intensity for (i).

Images of GFP-TRF1 labelled telomeres in UMUC bladder cancer cells. (a) Uncorrected images 23 µm below the cover slip. (b) Depth aberration corrected 23 µm below the cover slip. The correction assumed a sample index of 1.38 (c) Background subtracted profiles through the labelled telomere (bright spot in images a and b) along the axial direction. The dashed line is from the uncorrected image a, and the solid line is from the corrected image (b). The peak intensity in the corrected image is 60% larger over the background. The scale bar is 5 µm.

GFP labelled centromeres in eye Imaginal Discs in Drosophila embryos. Scale bar is 2 µm. (a) Maximum intensity projection of uncorrected three-dimensional data stack. Vertical is the axial direction. The top of the image is 2 µm below the cover slip and the bottom is 9 µm below the cover slip. (b) Maximum intensity projection of a depth aberration corrected data stack. The correction assumed a sample index of 1.38. (c) Line profiles along the axial direction for uncorrected (dashed line, open circles) and corrected (solid line, solid circles) images of a GFP labelled centromere.

Deconvolved images of alexa488-phalloidin labelled B16F10 mouse cells. Images are 4.4 µm below the cover slip. (a) Uncorrected image. (b) Uncorrected deconvolved image (c) image corrected by adaptive optics. The correction assumed a refractive index of 1.38 (d) image corrected by adaptive optics after deconvolution. The scale bar is 5 µm.

Maximum intensity projections of three-dimensional data stacks of 200 nm beads in agarose. The vertical direction is the axial direction and the total height of each image represents 22.5 µm. The width of each image is 34 µm. The arrows point to the position of the cover slip. Image (a) was taken using the piezo for focusing. Image (b) was taken using the DM to focus. The DM shape was set by using a sample refractive index of 1.34. (c) Shows close-ups, (i) and (ii), of the bead indicated by the red arrows in (a) and (b). The images are 1.6 µm × 8 µm (16 × 16 pixels) cross-sections in the xz-plane, scaled to maximum intensity.

Comparison of images taken by focusing with the DM (a) and mechanical focusing (b). Images are of C. elegans expressing a GFP sur-5 construct; the bright feature along the right side is the ventral nerve cord. The top images are taken 6 µm below the cover slip and the bottom images are xz-cross-sections. The difference in image intensity is due to photobleaching. Each image is scaled to its maximum intensity. A sample refractive index of 1.36 was assumed for focusing with the DM using . The scale bar is 2 µm.