Glare suppression by coherence gated negation

Imaging of a weak target hidden behind a scattering medium can be significantly confounded by glare. We report a method, termed coherence gated negation (CGN), that uses destructive optical interference to suppress glare and allow improved imaging of a weak target. As a demonstration, we show that by permuting through a set range of amplitude and phase values for a reference beam interfering with the optical field from the glare and target reflection, we can suppress glare by an order of magnitude, even when the optical wavefront is highly disordered. This strategy significantly departs from conventional coherence gating methods in that CGN actively 'gates out' the unwanted optical contributions while conventional methods 'gate in' the target optical signal. We further show that the CGN method can outperform conventional coherence gating image quality in certain scenarios by more effectively rejecting unwanted optical contributions. are within coherence gating technique uses an inversed coherence gating function gate out glare significantly, less

The ability to optically illuminate and image a target hidden behind a scattering medium is important in many applications, including transportation, remote sensing, biomedicine and astronomy. A classic example is the scenario of driving through fog at night with the automobile headlights on. The degradation of image quality in such scenarios can be generally ascribed to two effects: the optical wavefront distortion caused by the scattering medium and the glare from light backscattered from the scattering medium. The wavefront distortion limits our ability to perform diffraction-limited imaging and optical focusing. However, even in cases where the wavefront distortion does not prohibit imaging of the target, the sheer intensity of the glare can mask the weak optical reflection from a target and thereby prevent us from observing the target altogether.
Recent developments in wavefront shaping and adaptive optics have shown great promise in addressing the wavefront distortion challenge [1][2][3][4][5][6] . These methods have improved the imaging resolution beyond what was thought possible even a decade ago. However, in almost all of the demonstrations performed so far, the problem of glare is averted either by choosing a target that emits light at a different wavelength (fluorescence 7 or second harmonic generation 8 ) or by designing the experiments to operate in a transmission geometry. Glare remains a challenge largely unaddressed in the context of these developments. Unfortunately, glare is unavoidable in a variety of practical scenarios -driving in a foggy night is a good example. In that scenario, the objects you would like to observe are unlikely to be fluorescent, and you simply cannot rely on having an independent light source behind the objects to provide you with a transmission imaging geometry. Glare suppression in principle is possible using of time-of-flight methods with the help of fast imaging systems, such as those based on intensified charge-coupled device (ICCD) technology [9][10][11] or single photon avalanche diode (SPAD) arrays [12][13][14] . These devices are able to bin the light arriving at the detector with fine temporal resolution and therefore glare can be suppressed by discarding glare photons selected by their arrival time. Unfortunately, these instruments are very costly. But perhaps more importantly, the range to which they can suppress glare is determined by their response speed. The best commercial instruments available have a response time of 0.5 ns, which translates to a minimum length of ~10 cm for which they can suppress glare by time gating. Recently, SPAD arrays of temporal resolution of 67 ps have been demonstrated. However, they are currently only available in small array sizes (32 x 32 pixels) 13,15 .
There have also been some interesting developments on the use of modulated illumination and postdetection processing in the phase or frequency domain to achieve time-of-flight based gating 16,17 One significant limitation to these methods is that they need to contend with glare associated noise, as the glare is not suppressed prior to detection. Moreover, such techniques are limited by the frequency bandwidth of the sensors, which leads to a minimum length involved on the order of meters. This length limitation for all known glare countering methods precludes useful applications of such time-of-flight methods in biomedicine where the length scale of interest ranges from microns to millimeters.
The streak camera is yet another fast response optical detection system. Its response speed is on the order of one picosecond. Unfortunately, the streak camera is intrinsically a one-dimensional imaging system. Recently, it has been demonstrated that the use of compressed sensing can allow the streak camera to perform fast two-dimensional imaging 18,19 . However, the object sparsity constraint is too restrictive for the majority of glare suppression applications.
Here, we report a method, termed coherence gated negation (CGN), that is capable of coherently suppressing glare through the use of destructive interference to allow improved imaging of a weak target. This method can operate over a length scale span that is limited only by the coherence length of available optical sources, which can range from microns (for superluminescent diodes) to kilometers (for fiber lasers). CGN shares its roots with acoustic noise cancellation 20 . The basic idea is to use a reference optical field of the same magnitude and opposite phase to destructively interfere with the glare component of a returning optical field to null out the glare and its associated noise, thereby allowing the electronic detector to measure only the optical signal from the hidden target. In the case of acoustic noise cancellation, the amplitude and phase of the unwanted signal can be separately measured and used as input in the cancellation process. In CGN, we do not have this luxury as we do not have prior knowledge of the glare optical field characteristics. Here, we instead employ a light source of suitable coherence length such that a) the glare optical field is coherent with the reference optical field, and b) the target reflection is incoherent. By permuting through a specific set of amplitude and phase values for the reference field, we ensure that the condition for effective destructive interference is met within a certain error bound for one of the permutations. By screening for the minimum detected optical signal through the whole set, we can then determine the signal reflected from the target. When performed in an imaging context, this allows us to use a single permutation set operating over all the camera pixels at once to generate a glare suppressed image even if the optical field is highly disordered and speckled.
Using this approach, we experimentally demonstrate the ability to suppress the glare by a factor of 10 times with the use of a permutation set of size 256. Our experimental design choice also allowed us to demonstrate glare suppression on the length scale of 2 mm -a regime that conventional time-of-flight methods are presently unable to reach. Finally, we discuss the advantages and tradeoffs of CGN versus traditional coherence gating methods and report our experiments demonstrating CGN's ability to image targets at different depths without system alterations, and several scenarios where CGN can provide better target image quality than conventional coherence gating methods.

Principles
A concise setup to explain the principle of CGN is shown diagrammatically in Fig.1. A laser beam illuminates a two-dimensional target located behind a scattering sample. The returning light, which consists of light that is back-scattered by the scattering medium as well as light reflected from the target, is captured by the imaging system, resulting in an image of the target obscured by glare. On the camera sensor chip, the captured optical field is the superposition of the glare  choosing the coherence length of the laser source appropriately, we can make sure the glare contributions from the extended scattering medium are in coherence with the reference beam. As long as the optical path length of the target reflection is substantially different from the majority of the optical path lengths of the glare components, the target reflection will not be in coherence with the reference beam. We then permute the reference beam through a series of phase and amplitude changes. The observed image intensity for the ith image ( ) We further assume that the imaging is performed in such a way that the image speckle size is greater than the camera pixel size. This ensures that there are no phase variations across the surface of any given pixel. In this case, the minimum value that ( ) of the same magnitude and opposite phase of ( )  In practice, we do not expect complete destructive interference to occur as the glare optical field's phase and amplitude are continuously distributed, while the modulation of the reference phase and amplitude can only be performed in a discrete fashion. The greater the permutation set, the more effectively we can suppress the glare at the price of longer data collection time.

Experimental demonstration of glare suppression with CGN
To validate the CGN method, we implemented the experimental setup shown in Fig. 2a. A continuouswave laser (MGL-FN-532, Opto Engine, 532 nm wavelength, ~1mm coherence length) was used as the light source. Light from the laser was split into a reference and sample beam by a beamsplitter (CBS).
The sample beam illuminated the target, which was placed 2 mm behind the scattering sample (SS) (shown in Fig. 2a). The scattering sample (15 mm (x) × 25 mm (y) × 1 mm (z)) consisted of polystyrene particles (3 µm in diameter) in gel phantom (concentration 6.8×10 7 ml -1 , see Methods, sample preparation). The back-reflected light consisted of reflections from the target and glare from the scattering sample. On the other optical path, the reference beam was passed through an amplitude and phase modulator, spatially filtered, and collimated into a plane wave. The collimated reference beam illuminated the camera sensor chip at normal incidence. The reflected light from the target and the glare propagating through BS1 was captured by an objective lens (OBJ), filtered to a single polarization, and imaged by a tube lens (L1) onto the camera. The optical field's effective angular range was 6.3 degrees. This translates to an optical speckle spot size of 19.2 µm at the sensor. In comparison, the camera pixel size is 4.4 µm.
This allowed us to enforce the CGN operating requirement that the phase not vary substantially across any given pixel's surface. By path length matching, the collimated reference beam only interfered with the glare but not the reflection from the target. Before CGN was applied, an optical shutter (OS) blocked the reference beam, and an image of the target occluded by glare was captured as shown in Fig. 2c. The optical shutter was then opened and CGN applied. The reference beam was modulated through all permutations of 8 amplitude values and 32 phase values successively. After the reference beam went through all the permutations, a glare suppressed CGN image was acquired (Fig. 2d). Comparing the image before CGN (Fig. 2c) and after CGN (Fig. 2d), we can clearly discern the previously obscured target. To quantify the glare suppression ability of the CGN technique, we define the glare suppression factor as the ratio between the mean intensity of the glare before and after the CGN process. Through a null target experiment, we determined that the glare suppression factor was ~10 for this experiment.
Unsurprisingly, the glare wavefront was highly disordered. The glare wavefront as determined by the CGN process is reported in the Supplementary Information.  3b shows a histogram of the glare intensity before and after CGN for the situation where we permute through 10 amplitude steps and 32 phase steps. In this case, we experimentally achieved a glare suppression factor of ~30.

Comparison to coherence gating
By detecting only the optical field component that is coherent with the reference field, conventional coherence gating methods can also reject glare. However, the way in which conventional coherence gated (CG) and coherence gated negation (CGN) imaging methods work are opposite in nature. While CG imaging methods are good at 'gating in' an optical field originating from a specific chosen distance, CGN is good at 'gating out' the glare optical field. These different approaches to imaging in the presence of scattering and glare lead to two key distinctions between conventional CG methods [21][22][23]  To demonstrate CGN's advantage over CG in this aspect, we performed the following experiment. As shown in Fig. 4a, following the aforementioned procedure, CGN was applied to the target located at different positions A, B and C, which correspond to 1 mm, 2 mm, and 3 mm behind the scattering sample, respectively. Since CGN works by coherently gating out the glare component of the light, no adjustment is required to adapt to the depth change of the target, as long as the target remains within the depth of field of the imaging system. The experimental results are displayed in Fig. 4b-g. Fig. 4b-d are images of the target captured before glare suppression, while Fig. 4e-g are images captured after glare suppression.
From their comparison, we can easily discern that glare is suppressed and the visibility of the target is enhanced. The second key distinction between CG and CGN is that if an element contributing glare and a weak target object both lie within the coherence envelope of the light source, CGN can actually provide a superior signal-to-background image of the object. To clearly and simply explain this point, we consider a scattering sample as the glare contributor and a weak target placed at a distance L away from the CGN system. Here the coherence length of the light source is C, and L is set to be shorter than C. Under CGN operation, we adjust the path length to match the reference beam with the glare contribution. CGN will completely suppress the glare in this situation. As the target is partially coherent, we would expect a diminished signal associated with the target as only the incoherent portion of the target will contribute to image formation. In contrast, under conventional CG operation, we would match the reference beam path length to the target. This results in the detection of the target as well as a partial contribution from the coherent component of the glare. In aggregate, the CGN detection scheme results in a depressed target signal with no glare background, which is more desirable than the CG case where a glare background is present. This result is also valid over the range of an extended scattering media.
To demonstrate CGN's advantage, we performed the following experiment. As shown in Fig. 5a, a thin scattering medium (15 mm (x) × 25 mm (y) × 0.5 mm (z)) consisting of polystyrene particles (3 µm in diameter) in a gel phantom (concentration 6.8×10 7 ml -1 , see Methods, Sample preparation) was attached directly on the top of a reflective target. CGN was applied after the path length of the reference beam was matched with the glare as shown in Fig. 5b. Images of the target acquired before and after CGN are included in Fig. 5c and Fig. 5d, respectively. After these images were acquired, the path length of the reference beam was adjusted to match the reflection from the target and phase shifting holography 24 was applied as a demonstration of a CG approach. The retrieved intensity map from this procedure is shown in

Discussion
In this series of experiments we demonstrated the differences and advantages of CGN compared to hardware based time-of-flight glare reduction systems and conventional coherence gating methods.
CGN's ability to suppress glare over optical distances as short as several microns through the use of low coherence light sources, such as superluminescent diodes, contrasts favorably compared to conventional time-of-flight hardware. We also showed that, by suppressing glare and permitting all other optical signals to pass, CGN allows for the simultaneous imaging of objects at different distances. In contrast, CG methods are good at imaging objects at a given distance and rejecting optical contributions before and after the chosen plane. We further showed that CGN can outperform CG methods in image quality under certain conditions -specifically, when the glare components and the target optical field are within the same coherence window of the interferometer.
The CGN design for a specific application will be application dependent. For example, in the scenario where we would like to cancel glare from a fast changing scattering medium, we would likely need both a fast camera and a fast reference field permutation apparatus. Alternately, in this scenario, we may instead choose to perform CGN in a pixel-by-pixel basis rather than a full-frame basis. For pixel-by-pixel CGN, we would focus on a single pixel and iteratively derive the correct reference cancellation field quickly. In an ideal situation, we would only need a few measurements to arrive at the correct field 25,26 . By performing CGN this way, we can progressively work through all the image pixels. As long as the time taken to optimize glare suppression for each pixel is shorter than the time scale at which the scattering medium is decorrelating its optical field, we can expect to suppress glare effectively.

Sample preparation
Polystyrene microspheres with a mean diameter of 3 µm (Polybead Microsphere, Polysciences, Inc.) were mixed with a 1.5% carrageenan gel in aqueous phase. The mixture was cast in a mold of size 15 mm × 25 mm, with a thickness of 1 mm or 0.5 mm. The medium had a theoretically calculated scattering coefficient of µ s =σ s N=1.3 mm -1 , where the density of the microspheres N is 6.8×10 7 ml -1 and the scattering cross section σ s is 18.7 µm 2 .
The target was made by attaching a positive mask showing letters "Hi" to an optical mirror. The height of the letter 'H' was 1 mm.

Setup
The experiment was carried out on a custom-built setup as depicted in Fig. 2a. A continuous-wave laser (MGL-FN-532, Opto Engine) with 532 nm wavelength and a coherence length of ~1mm was used as the light source to illuminate the target. A laser with long coherence length (Excelsior 532, Spectra Physics, 532 nm wavelength, >9 m coherence length) was used only for characterizing the glare (Fig. 3). Light from the laser was split into a reference beam and a sample beam by a beamsplitter (CBS). The sample beam illuminated the target at 2 mm behind the scattering sample (SS) (shown in Fig. 2a) The path length of the reference beam matched with that of the light reflected from the scattering sample.