1.1.

Problems Presented with AO/SS-OCT

There is a trend in developing long coherence length swept sources that can determine an axial range extending over 1 cm and more.⁹ On the other hand, an AO enhanced confocal microscope system can shrink the confocal profile width to values of tens of micrometers or even smaller. As the SS-OCT method presents the disadvantage that the reflectance of all points along the axial range are measured under a fixed focus, maximum sensitivity within the cross-sectional (B-scan) OCT image is achieved in the focus only. If the full width at half maximum (FWHM) of the confocal profile acting as a confocal gate (CG) is smaller than the OCT axial range (AR), then the OCT image presents high contrast and good transversal resolution within a spatially restricted stripe determined by the CG only.

1.2.

Possible Solution

The problem presented is that the region of highest quality (as determined by contrast and resolution) is limited by the width and position of the CG. Efforts have been made to extend the depth of focus (DOF) while maintaining high lateral resolution. One approach uses an axicon lens to produce a Bessel beam, extending the DOF when compared with a Gaussian beam. The DOF is enlarged at the expense of lowered sensitivity, making the method less suitable for imaging samples of low reflectance,^10,11 although progress has been made to improve its efficiency.¹²

A solution was developed based on Gabor filtering¹³ that shifts the CG incrementally through the sample; an OCT cross-sectional image was acquired at five different focus positions (R) as manipulated by an electrical lens. From each of the five images, the in-focus region was extracted and then spliced together to form a single image wherein all regions are in focus.

It was determined that five repetitions of data acquisition with shifted focus were sufficient as the CG profile was approximately one-fifth of the AR. Due to the enhanced coherence length of swept sources, the ratio $R=\mathrm{AR}/\mathrm{CG}$ may be much larger than 5, in which case the Gabor procedure may considerably slow the acquisition. This presents a problem as the process is largely manual, with the margin for error increasing as there may be variations in the imaging parameters over time, especially with living samples. The next logical step would be the design of a system that simplifies and expedites this procedure.

2.1.

Concept

Given the speed of SS-OCT imaging which allows frame rates as high as 100 Hz, there is room for sufficiently high values of R to still secure a video rate, which is important in live imaging systems.¹⁷ R B-scans are acquired where the region of maximum intensity as determined by the CG profile is shifted deeper within the object along the z coordinate. After acquisition, each image obtained in this way may then be cropped to isolate the in-focus regions in depth. The cropped images are subsequently assembled together across R into a single synthesized image of uniform intensity.

The focus control using a DM is achieved by generating a set of corrections by controlling the magnitude of the Zernike polynomial responsible for that of defocus only. Closed-loop correction will be conducted to optimize the wavefront, providing a base configuration for the DM. The focus will then be shifted and the closed loop executed again to achieve optimization at the new position. This will provide two states (base and modified states) from which intermediate positions may be interpolated. In essence, we would have a set of states where the corrections have been optimized for imaging at different axial positions in the sample.

2.2.

Optical Design for Minimizing System-Induced Aberrations

This implementation of DM control utilizes a system of passive and active aberration correction to improve image quality. Passive correction is achieved through an optimized system wherein the number of optical elements (specifically the curved mirrors required to resize the beam, known for inducing aberrations) has been minimized. Collimators (Schafter and Kirchhoff: FC-F-4-M15-37) launch beams of 3 mm diameter.

By using the two galvoscanners, X and Y (5 mm), close to each other, the number of curved mirrors is reduced. Two telescopes (pairs of curved mirrors with different focal lengths) are placed in the setup to increase the beam diameter to 15 mm to fully cover the reflective surface of a DM (Imagine Optics: Mirao-52e), and then to reduce the beam down to 7.5 mm on the final lens (L2) of the 25-mm focal length.

Furthermore, these telescopes are arranged in a nonplanar configuration with the beam propagating in a single plane, either horizontally or vertically. This is seen in Fig. 1 where the beam travels between curved mirrors CM1 and CM2 in the plane Y, with no deviation in X. The beam is then propagated horizontally across the surface of the DM and then vertically to CM4, at the same elevation with CM1. This technique has been shown to compensate for astigmatism aberrations induced by reflections from curved mirrors.¹⁸ We measured the sensitivity of the OCT setup to be 100 dB using previously reported techniques.¹⁹ The numerical aperture of the system was calculated to be 0.175. For imaging, we use a 100-kHz Axsun swept source with a central wavelength at 1060 nm.

We experimentally determine the field of view by blocking the reference arm (using the confocal signal only) to image a large bar on the United States Air Force (USAF) resolution target. For this measurement, the DC output of one photodetector from the balanced detector was used. The target is mounted on an XYZ translation stage, allowing movement of the bar to the limits of the displayed image and measurement of the displacement using the micrometer screws. From this, we determine that for an amplitude of 1 V of driving signals applied to both scanners we achieve a $700\times 700{\mu \mathrm{m}}^2$ raster size, and with a 0.1 V amplitude the area is $70\times 70{\mu \mathrm{m}}^2$.

2.3.

Active Aberration Compensation Using Deformable Mirror

Active wavefront correction is achieved using a single 52-actuator MEMS DM in conjunction with a Shack–Hartmann sensor (Imagine Optics: HASO-32). Wavefront sensing is performed using light from a 830-nm broadband super luminescent diode (SLD), whose beam path is almost completely shared with the 1060-nm imaging arm. Prior to imaging, using a scattering target such as paper, correction is achieved that brings the DM into an optimal starting configuration where any residual aberrations induced by the optical elements in the system itself are reduced.

With the inclusion of tilts and focus in the wavefront error calculations, we are able to achieve a wavefront roor-mean-square (RMS) value better than $0.2\mu \mathrm{m}$. After a stable correction is achieved, the voltage values applied to the DM are saved into an XML file. This file contains a one-dimensional (1-D) array of 52 numerical values, each corresponding to a single actuator on the DM. The values of this array represent the voltage settings of the 52 actuators on the DM that achieve the best wavefront correction. This set is considered a base state, i.e., the midpoint of the axial imaging range to be used next.

2.4.

Shifting the Confocal Gate

The next stage is to modify the amplitude of a single Zernike polynomial, in this case that of defocus is selected, to a different value. This causes the mirror to adjust its shape to add defocus aberration in addition to its corrected state. With defocus added, the closed loop is executed again to compensate for the possible increase in other aberrations caused by manipulation of the focus. No other types of aberrations are directly added in this way, so it can be assumed that the difference between the original base state and the modified state is the addition of defocus only. Again, the modified state file is a 1-D array of 52 values, this time representing the position of every actuator on the DM to form a state with a modified focus. This modified state file is also saved along with the original base state file.

Given that the linearity of the DM is greater than 95%,²⁰ the difference between the base state and the modified state is a linear increase in defocus aberration. Custom software programmed in LabVIEW dynamically interpolates a two-dimensional (2-D) array of intermediate voltage values for every actuator using these two 1-D arrays. The size of the 2-D array is R by 52, where R is the number of steps required. Each successive column in this 2-D array contains a complete set of 52 actuator voltage values, representing an incremental shift in focus.

This 2-D array can be expanded to any size and any range of focus, limited only by the speed and stroke of the DM, respectively. A larger array may impact the rate at which the DM actuates the commands. Increasing the size of the array (number of columns) will adjust the number of incremental steps (R) between two user-defined limits. Shifting the confocal gate by $40\mu \mathrm{m}$ in 50 steps covers a 2 mm range as experimentally determined using a mirror as an object and finding the new focus position for the deformed state of the DM.

Adjusting the limits of the array affects the magnitude of defocus aberration applied to the DM; in this way, the AR can be dynamically adjusted while scanning to suit the sample thickness. To produce a smooth focus sweep at a consistent rate, we typically make these limits symmetrical, i.e., between $-1$ and 1 mm with the midpoint representing zero defocus added. The visible effect on the image is a sweeping region of high intensity through the depth range of the sample.

2.5.

Analysis of the Confocal Profile and Signal Strength During Focus Sweep

It is important to determine how the confocal profile is affected as we shift the focus through the sample. To test the imaging performance, we set the DM to assume the base state corrected configuration. During the measurement, we set the AO to run in open loop, i.e., the corrections are maintained without feedback from the wavefront sensor (WFS). In this mode, we may still directly manipulate the mirror to add defocus.

A mirror is mounted on a XYZ translation stage and placed as the object in the imaging arm. We block the reference arm and use the confocal signal (with weak light emitted from the SLD to avoid saturating the detector) to determine the confocal profile of the system at this default state. The DM is then set to add different values of defocus in increments of $1\mu \mathrm{m}$ RMS. For each new focus adjustment, the translation stage with the mirror was moved around the focussed position and the strength of the confocal signal was measured to construct the confocal gate profile.

Confocal profiles for three focus adjustments are shown in Fig. 2. From the graphs, we can ascertain two critical facts about the focus sweep. First, it is clear that the image intensity drops as the DM introduces more defocus.

Fig. 2

Chart showing how the confocal profile shifts in depth and changes shape as we add 1 and $2\mu \mathrm{m}$ RMS focus.

Second, it is important to note that the width of the profile increases with defocus. We start with a FWHM of $60\mu \mathrm{m}$ in the base state, which first spreads to a FWHM $70\mu \mathrm{m}$ as defocus aberration is increased to $1\mu \mathrm{m}$ RMS, and then spreads further to FWHM $80\mu \mathrm{m}$ with $2\mu \mathrm{m}$ RMS defocus. The enlargement of the confocal profile and reduction of its maximum with the defocus applied suggest deterioration of the correction. Naturally, this would decrease the depth resolution of the confocal microscope (the object arm), though this is not a concern with OCT imaging.

The sensitivity decay with defocus is quantified for larger defocus values in Fig. 3. In this case, for each defocus value applied by the DM, the object mirror was moved back into focus using the translation stage and the strength of the confocal signal was measured. There appears to be a sharp drop as the focus first moved from base state, and then recorded intensity decreases below 50% for $\pm 3\mu \mathrm{m}$ RMS defocus, reaching 10% for $\pm 8\mu \mathrm{m}$ RMS defocus. The power profile is shown as a symmetric around base state when adding positive or negative focus.

Fig. 3

Chart showing decay in signal intensity with added focus.

The chart in Fig. 3 can be used to select a useful range to operate the DM where the sensitivity loss can be tolerated for a given imaging object. This sensitivity loss is a limitation of this technique and is not observed with other methods of focus control such as using an electrical lens.

From the data shown in Fig. 2, it is clear that applying $1\text{-}\mu \mathrm{m}$ RMS defocus equates to an axial shift of the focus by $250\mu \mathrm{m}$; therefore, a sweep between $-2$ and $2\mu \mathrm{m}$ RMS would offer a 1-mm axial imaging range.

2.6.

Assessment of the Transversal Resolution

To test practical image resolution, an image is acquired of a USAF 1951 target, as shown in Fig. 4. We know from the data shown in Sec. 2.2 that for driving signals of 0.1 V amplitude applied to both scanners we achieve a scan area of $70\times 70{\mu \mathrm{m}}^2$ on the sample. Given an image size of $250\times 250$ pixels, it can be deduced that each pixel covers $0.28\mu \mathrm{m}$ along the horizontal and vertical directions.

Fig. 4

High contrast confocal image of the USAF target showing the smallest $2\mu \mathrm{m}$ bars at the bottom. Two sets of three bars are shown horizontally and vertically oriented. Image size is $250\times 250$ pixels covering an actual area of $70\times 70\mu \mathrm{m}$ on the target.

Figure 4 shows an image of the USAF target where two sets of three bars (each $\sim 2\mu \mathrm{m}$ apart) are shown distributed both vertically and horizontally. Given the parameters described above, we may analyze the distance between the bars in pixels to determine the actual spacing in $\mu \mathrm{m}$. Both the horizontal and vertical bars are shown to be 7 pixels apart: $7\times 0.32=1.96\mu \mathrm{m}$ apart. This confirms our reported transversal resolution values.

To determine how lateral resolution is affected when axially shifting the CG, the USAF 1951 resolution target is used as the object and images are acquired for different defocus values. Initially, we assume the base state with no defocus, and position the object such that the set containing the smallest bars (of $2\mu \mathrm{m}$ spacing) is within the center of the frame. Figure 5 shows four additional images taken of the same region of the target, with different levels of defocus applied to the DM. Each time defocus is applied to the DM, the USAF target is manually moved axially back into focus before acquiring the image. The distance between the bars in the images obtained with focuses $-1$, 1, and 2 (focus moved at $-250$, $+250$, and $+500\mu \mathrm{m}$, respectively) are the same as in the image at focus 0. There appears to be a loss in signal intensity in the image acquired with focus $-2$ ($-500\mu \mathrm{m}$), which is not apparent in the others, but the transversal resolution seems intact.

Fig. 5

Effect of defocus on the image acquired from the USAF target, using the same area as in Fig. 4. The original image (c) is repeated in (d) and placed alongside images taken with $-2$ (a), $-1$ (b), 1 (e) and 2 (f) $\mu \mathrm{m}$ RMS focus added to the deformable mirror (DM).

Some lateral drift is also identified, seen by the bars moving across the image as the focus is changed. From 5(c) to 5(b), the bars moved up by 7 pixels and from 5(b) to 5(a) by a further 7 pixels. From 5(d) to 5(e), the bars moved down by 7 pixels, and from 5(e) to 5(f), by a further 7 pixels. Seven pixels’ vertical shift means $2\mu \mathrm{m}$, i.e., comparable and larger than the transversal resolution. In terms of the horizontal shift of the image, from 5(c) to 5(b) there is a slight shift of 1 pixel, while from 5(b) to 5(a) there is shift of 7 pixels to the left. From 5(d) to 5(e), there is a lateral shift to the right of 7 pixels and from 5(e) to 5(f) an additional 7 pixels to the right.

The experiments reported in Sec. 2.5 show that the variation of focus imprinted by the DM when obtaining the images in Fig. 5 covers a 1-mm axial range. Using the same process described above, the effect of applying larger defocus values to the DM is evaluated by the resolution in the images acquired, shown in Fig. 6.

Fig. 6

Images of the USAF target obtained using the DM deformed to create $3\mu \mathrm{m}$ (b) and $4\mu \mathrm{m}$ (c) RMS defocus, with the original $0\mu \mathrm{m}$ focus image (a) for comparison.

In the image in Fig. 6(b), the bars moved to the right by 24 pixels (top of the bar barely visible), i.e., by $6.9\mu \mathrm{m}$. In the image in 6(c), the bars moved to the right by 28 pixels, i.e., by $8\mu \mathrm{m}$. In terms of vertical shift, the bars moved down in 6(b) by 21 pixels and in 6(c) by 28 pixels. On average, from images in Figs. 5 and 6, it can be inferred that each $1\mu \mathrm{m}$ defocus shifts the image down and to the right by approximately 7 pixels and each $-1\mu \mathrm{m}$ defocus shifts the image up and to the left by approximately 7 pixels, i.e., $2\mu \mathrm{m}$ or a resolution interval.

In conclusion, RMS focus control via the DM in the configuration assembled has a pronounced effect on the lateral drift. It is important to note here that the lateral resolution as determined by the horizontal bars appears to remain unaffected, though the vertical bars have become distorted and blurry. Practically, a good signal is obtained from the central part of the image only. We believe this is due to the fact that the correction file was taken with the scanners in a zeroed position, meaning the corrections are less valid for the periphery of the imaged area.

Some lateral shift is expected due to the off axis configuration, typical in AO systems using DMs. This can be further reduced by increasing the focal length of the spherical mirrors CM2 and CM3, with the obvious disadvantage of enlarging the size of the layout and a reduction in the axial range covered. Another factor is the imaging beam potentially being slightly off-axis to the USAF target. A combination of these two factors may be responsible for the slight horizontal shift between images in Figs. 5(b) and 5(c). We noticed that by tilting the USAF target, the lateral shifts change. This prevents postprocessing compensation by software.

2.7.

Effect upon Wavefront When Manipulating Focus

In-depth analysis of the effect of focus manipulation on other aberrations was conducted. WFS measurements are taken as the DM is set to varying levels of defocus. Figure 7 shows the overall wavefront error as detected by the WFS, with focus varied between $-0.5$ and 0.5 mm. It can be observed that tilt significantly contributes to the overall wavefront error in comparison to the other aberrations. It can also be inferred from the chart that the total wavefront error excluding defocus is five times less than the value with defocus. This demonstrates that the contribution of defocus to wavefront error is much greater than the aberrations that increase as a consequence of focus manipulation.

Fig. 7

Root mean square (RMS) wavefront error as focus is manipulated. Total error: green region. Error excluding focus: blue region. Error excluding tilts and focus: red region.

A breakdown of the first eight aberrations is shown in Fig. 8, where it can be seen that all these aberrations increase as defocus is applied in either direction. Defocus aberration is plotted for the reference (green), and appears linear as expected. The red and blue dashed lines represent fluctuating tilts 0 and 90, respectively, and seem to exhibit the highest variance.

Fig. 8

Effect of focus manipulation on defocus aberration (green) and on seven other high-order aberrations (according to color in the inset).

Figure 9 displays the RMS error for the data in Fig. 8, excluding the tilts and focus aberrations. From this graph, it is seen that the effect of focus manipulation on these aberrations is within a range between $-0.1$ and $0.07\mu \mathrm{m}$ RMS. It is possible that these larger values at the extremeties of the range are due to the limited dynamic range of the DM used. If this is the case, these can be made smaller if a second wavefront corrector is employed.

Fig. 9

Magnified view of WFS RMS error showing effect of focus on wavefront excluding tilts and focus aberrations.

2.8.

Test Procedure

Measurements to test the procedure are conducted on a phantom target constructed using 10 layers of borosilicate glass microscope slide covers, each of thickness between 0.16 to 0.19 mm. Each slide was bound using a single layer of thin clear tape. As the clear tape is extremely thin, distances between the slides are not resolved and so, only 11 interfaces should be distinguished. As seen in Fig. 10, even after some tilt, extra layers appear at the bottom and some layers in between the main interfaces, due to multiple reflections between the slide facets. The total thickness of the sample is approximately 2 mm.

Fig. 10

Images acquired of a phantom constructed from ten 0.17-mm thick glass slides (bound top and bottom with sellotape of similar thickness) with focus set to $-4$ (a), 0 (b) and 4 (c) covering a total range of 2 mm. The final image (d) is synthesized through extraction of in-focus regions from a stack of images acquired with focus incrementally shifted.

During live imaging, a sequence of commands is sent to the DM in rapid succession, with an optional time delay between each command. The magnitude of defocus aberration is swept between the limits of $\pm 4\mu \mathrm{m}$ RMS using the DM (determining an axial range of 2 mm in depth). The procedure was tested with 50 steps of $40\mu \mathrm{m}$ each at a rate of 200 commands sent to the DM per second. Oversampling by using a high number of small steps was found to produce a smoother focus transition. Transversal size was maintained at 1 mm and the refresh of the B-scan OCT imaging was 100 Hz.