Shack–Hartmann wavefront sensors (SH-WFSs) [1] have been used extensively to provide direct wavefront sensing in close-loop adaptive optics (AO)–assisted imaging techniques [2]. Current SH-WFSs exhibit a large depth range and therefore cannot measure depth-resolved wavefronts. For the same reason, they are vulnerable to stray reflections from the imaging system and the targets. Direct wavefront sensing was deemed unsuitable for microscopy because of the lack of a single point-like reference source [3,4]. In addition, multiple facets of multielements in the microscope objective and multiple reflections from the microscope slides produce strong stray light onto the camera. Such stray reflections create additional spots to the useful spot pattern that confuse slope calculations. There is no simple way to distinguish such spots from the spots that result from the sample. For indirect wavefront sensing, algorithms to maximize sharpness metrics, such as simulated annealing [5] and genetic algorithms [6] have been devised to infer the correction required; however, these usually require several minutes for each point to find the optimum correction [7,8]. Principles of low-coherence interferometry (LCI) have been added to a virtual SH-WFS to narrow its depth range [9,10]. To this goal, a virtual lenslet algorithm was applied to three-dimensional (3D) data collected by an LCI from backscattered light. Similar to an indirect WFS, this numeric coherence gate (CG) method involves a large quantity of computations, which demand long processing time.

In this Letter, we present results using a different approach, where coherence gating was applied directly onto the beams produced by a physical lenslet array (LA). This method has the advantage of much higher speed and can be developed to perform dynamic measurements, as required for fast moving targets in microscopy or for human retinas. In a previous report [11], it was demonstrated that the principle of an SH-WFS is compatible with two formats of implementing a CG, operating in time domain using a broadband optical source and phase-shifting interferometry (PSI) [12], and operating in spectral domain using narrow-band wavelength-scanning interferometry. For this demonstration, we chose the time-domain approach, because it is more intuitive, providing en-face images of SH spots directly. Here, to the best of our knowledge, we demonstrate for the first time the capability of a CG/SH-WFS to measure depth-resolved wavefronts from multiple layer targets in real time, in the presence of strong stray reflections.

The experimental setup of the CG/SH-WFS is illustrated in Fig. 1. A superluminescent diode (SLD), with a central wavelength of 850 nm and an FWHM bandwidth of 20 nm is used as the optical source, determining an axial CG of 16 μm in air. A beam of 10 mm diameter is launched from the SLD by a collimating lens, CL, onto a beam splitter, BS1. Light is divided into an object beam and a reference beam, which are focused by two achromatic doublets, L1 and L2, of focal length 30 mm onto the object, Obj, and onto a reference mirror, RM, respectively. The Obj is mounted on an object translation stage, OTS. The RM is mounted on a Piezo-actuator, PZT, which is driven by a generator, G, to introduce phase modulation. The three elements, L2, RM, and PZT, are mounted together on a reference translation stage, RTS, that provides axial movement to change the optical length of the reference path. On the return path, both the reference and object beams are reflected once more by the two beam splitters, BS2 and BS3, respectively. The two beams then recombine at another beam splitter BS4. Between the BS3 and BS4 in the object path, an LA (Thorlabs MLA300-14AR) samples the incoming object beam laterally. A telescope (L3 and L4 of focal length 75 mm and 100 cm, respectively) relays the foci of the LA to a CMOS camera (CMOS; Mikrotron EoSens CL, MC1362, $1280\times 1024$ pixels). When the optical path lengths of the object and reference arms are matched, interference takes place between the reference beam and the converging beams produced by the LA. The camera acquisitions are synchronized with the light source to apply stroboscopic illumination. Four-step PSI [13] was employed to retrieve en-face depth-resolved coherence-gated images of the SH spots. Therefore, the maximum frame rate of the coherence-gated acquisition is 125 fps, a quarter of the maximum frame rate of the camera. For each en-face image of spots, four images of intensity $I_i$, with $i=1$ to 4 are obtained by incrementing the phase shift in steps of $\pi /2$ using the PZT. Then, the intensity of the CG/SH-WFS image is obtained by using the following formula:

 

Fig. 1. CG/SH-WFS setup. SLD, superluminiscent diode; CL, collimating lens; BS1, BS2, BS3, BS4, four plate beamsplitters; RM, reference mirror; Obj, object, made of two nonparallel microscope slides of 1.4 mm thickness mounted in front of a mirror, OM, as shown in the inset; PZT, Piezo-actuator; RTS and OTS, reference and object translation stage, respectively (moving axially); L1, L2, L3, L4, achromatic doublets; LA, lenslet array; P1, P2, P3, P4, and P5 in the inset, the five planes in the Obj where wavefronts originate from.

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Standard SH-WFS images were collected by inserting a stop in the reference path of the interferometer (between BS2 and BS4 in Fig. 1). In all experiments, matrices of $17\times 17$ SH spots in the central area of spot images were selected to reconstruct the wavefronts and calculate the aberrations. A window of $22\text{pixels}\times 22\text{pixels}$ was allocated to each spot.

Initially, a direct SH-WFS image was acquired from a mirror, OM, which was placed in the focus of lens L1. The reference beam was blocked. This image is considered to be a reference of SH spots pattern, which is required to calculate the wavefront slopes. The focus position is found in cases in which the intensity of the spots is maximized by shifting the OTS. Then, we unblocked the reference beam and applied a four-step PSI algorithm to produce CG/SH-WFS images of nodes. The reference path length was adjusted (by translating the RM using the RTS) to move the axial position of the CG to match the location of OM, where the optical path difference (OPD) is zero. When $\mathrm{OPD}=0$ is achieved, the intensity of the SH spots in the coherence-gated image is at a maximum. In the following experiments, the RM is kept in this position. A multilayer object, Obj (Fig. 1. inset), is assembled using two thin microscope slides (approximately 1.4 mm thick) mounted at some distance above the OM. The two slides contribute to four more interfaces, P1, P2, P3, and P4, respectively, corresponding to discontinuities from air to glass in the index of refraction. To introduce aberrations, the two slides are deliberately tilted by a small angle ($<0.025\mathrm{rad}$) in relation to each other. A fifth interface, P5, is due to the OM, placed approximately 1.7 mm away from the second plate. In what follows, this interface is used as a dominant reflector in comparison with the other much weaker reflections from the other four interfaces. The five-layer Obj was placed on the OTS. The first interface, P1, was measured at an axial position $\mathrm{OPD}=0$ (the OM’s initial location) and at the point at which the CG coincides with the focus. Then, the whole object is moved toward BS3 by translating the OTS until the $\mathrm{OPD}=0$ condition is regained at each other interface. The corresponding set of spots is acquired for each plane in the Obj, and hence five groups of data are acquired.

For each so-selected axial position of the Obj, chopped zoomed images of CG/SH-WFS are shown in the bottom row in Fig. 2. Corresponding standard SH-WFS images are shown in the top row in Fig. 2, obtained by blocking the reference beam and displaying the images directly (no PSI algorithm). The standard SH-WFS images display spots because the planeis in focus, superposed on spots due to the other layers, with the brightest spots resulting from OM reflections, which dominate all other spots. By moving the Obj axially, the bright reflections from the OM diminish and spread to the SH spots pattern. Despite the fact that the reflections from the selected depths are much dimmer in comparison to the bright reflections from the OM, they are clearly selected by the CG, as can be seen by comparatively inspecting the images Fig. 2(a) and Fig. 2(f), Fig. 2(b) and Fig. 2(g), Fig. 2(c) and Fig. 2(h), and Fig. 2(d) and Fig. 2(i).

 

Fig. 2. Zoom images collected from the SH spots obtained with the SH-WFS in (a)–(e) and with the CG/SH-WFS in (f)–(j). In each column, the Obj was moved until P1, P2, P3, P4, and P5 planes matched each of the $\mathrm{OPD}=0$ conditions, respectively.

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The images in the top row in Fig. 2 illustrate the inability of a standard SH-WFS to provide wavefront measurements from a structure made of low-reflective scatterers in the presence of a strongly reflective layer, the OM. In such a case, even if the conventional SH-WFS is made operational by thresholding the intensity of spots, the overall wavefront aberration is dominated by the signals from the high reflective layer. The spots from other depths may be included in the centroiding algorithm and induce errors in the wavefront measurement. In opposition, in all CG/SH-WFS images [Figs. 2(f)–2(j)], only one group of spots is visible. The reflections from other layers, including those from the OM, are totally eliminated, that is, the number of spots in the coherence image is consistent and correct.

The spots produced by the CG/SH-WFS (corresponding to a single layer in the Obj) were then used to synthesize the wavefront and evaluate the aberrations in terms of Zernike polynomials [14], as shown in Fig. 3. The most important are the second, the third, and the fifth coefficients, which are responsible for tilt along $x$ direction, tilt along $y$ direction, and defocus, respectively.

 

Fig. 3. Reconstructed wavefronts from all five layers of the object, (a), (b), (c), (d), and (e), are the wavefronts measured from P1, P2, P3, P4, and P5, respectively; (f) displays the first 13 Zernike coefficients for all measurements.

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The image Fig. 3(a) was recorded at the axial location where the CG coincides with the focus. When moving the Obj toward BS3 to obtain $\mathrm{OPD}=0$ for the rest of the planes, the focus position moves away from BS3, whereas the CG moves toward BS3, that is, the focus and the CG translate in opposite directions. Therefore, in the process of regaining the $\mathrm{OPD}=0$ at each interface, the axial movement of the whole Obj leads to a mismatch between the axial position of the plane selected by the CG/SH-WFS and the position where the focus should be. This means that only Fig. 3(a) was acquired without sample-induced defocus aberration. In all other images, Figs. 3(b), 3(c), 3(d), and 3(e), the CG and the focus differ, with the focus moved away from BS3. The fifth Zernike coefficients in Fig. 3(f) show the smallest value for P1, where the CG was superposed on the focus, whereas larger values are obtained for the P2 and P3 and even larger for the P4 and P5. Their comparative values are in agreement with the expectations, because the mismatch between the CG and the focus increases from P2 to P5. Because of the similar differences between the focus position and the CG position for the P2 and P3, similar results were obtained for the fifth coefficient. For the same reason, the values of the fifth coefficient for the P4 and P5 are also similar. The results in Fig. 3 also show that aberrations of tilts in the $x$ direction (the second Zernike coefficient) are larger than those in the $y$ direction (the third Zernike coefficient) because of the deliberate tilting of the top slide in the Obj when it was assembled. These results confirm that measurements of depth-resolved wavefront aberrations are possible from different layers in depth in the same object.

In summary, real-time operation of a CG/SH-WFS setup is demonstrated, capable of producing similar spot patterns as a conventional SH-WFS, from a five-layer target. SH spots from each layer are selected in depth in the presence of stray reflections from the other layers, including strong reflections from one of the layers, a mirror. Depth-resolved wavefront measurements and analysis are demonstrated, from each of the five layers based on each set of SH spots separated by the CG. For the example of the object used, a conventional SH-WFS could not deliver aberration information except from the layer providing strong spots (i.e., the mirror), as too many sets of spots of similar intensity were present in the image. These results are relevant for developing WFSs to be applied to AO microscopy of thick samples. The capability of depth-resolved aberration measurement may lead to new approaches of wavefront correction in AO-assisted ophthalmology. Further work is required to validate the method in imaging scattering targets.