1. Introduction

Dielectric mirrors, or sub-wavelength-scale layered structures that cause selective reflection and interference of light, play an important role in oceanic camouflage in large, fast animals such as fishes and squids. Since their large, muscular bodies apparently do not allow the common pelagic adaptation of transparency, these animals employ reflectivity to hide them in their void-like environment. Their reflective, iridescent appearance is due to specialized dermal structures called iridophores [1]. Iridophores consist of layers of high and low refractive index materials that interact with incident light to produce the observed reflections. In fish, the high index layers are made of guanine, while in squids they are proteinaceous [2]. The orientation, index of refraction, and thickness of each layer in the stack determines the spectrum and directionality of reflected light.

The adaptive value of these structures has been previously explained as relatively simple mirroring [1–6]. However, because biological systems have precise control of geometry at sub-micron spatial scales, reflection from these structures can be quite complex compared to simple one- and two-dimensional dielectric structures [7, 8]. Therefore, the camouflage strategies used by these animals seem likely to be more sophisticated than that provided by a simple mirror. In the open ocean, vertical mirrors can provide camouflage for flat surfaces in some situations, but fast-swimming animals require rounded sides for hydrodynamic considerations. Under certain geometries, specular flashes will cause a mirrored curved surface to be quite conspicuous [6]. Initial studies performed on silvery fish [2, 3] showed that the reflective structures can be organized to compensate for this problem. This adaptation effectively produces a flat mirror over the entire curved body of a fish. However, it is unclear if this is a general strategy for the majority of reflective pelagic organisms. In addition to geometrically and chromatically complex reflection from iridophores, animal camouflage is modulated by chromatophores, or dynamic light-absorbing cells, in the case of both fishes and squids. Radiation in the open ocean is complex in both geometry and wavelength, and an ideal reflective camouflage must also account for these complexities.

The role of dynamically changing optical conditions has also been considered in the context of marine animal camouflage [4–6]. Measured inherent ocean optical properties were combined with radiative transfer models to determine realistic underwater radiance distributions. The results were in turn used to estimate optimal reflectance spectra for pelagic camouflage under a variety of viewing conditions. Known visual response of a specific predator was used to complete the simulations. These comprehensive analyses improved understanding of the situations in which certain types of optical camouflage are ideal, and allowed the researchers to offer potential explanations for observed foraging strategies in pelagic habitats.

To better understand the principles under which reflective structures in fishes and squids operate, and to determine whether something more sophisticated than simple mirroring has evolved, a detailed characterization of their optical properties is required. To describe object appearance in a given light field, an underlying function, the bidirectional reflectance distribution function (BRDF), has played a fundamental role. The BRDF, with parameters defined as shown in Fig. 1, is specified at a point and is defined as the reflected radiance L_o from a surface divided by the incident irradiance E_i, and can be written

 

Fig. 1 Definition of the bidirectional reflectance distribution function (BRDF) parameters. Subscripts i and o represent incident and viewing (outgoing) angles respectively.

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Using models constructed from directional reflectance function measurements of organic surfaces, it is possible to make conclusions about the organisms and learn the physical strategies animals use for camouflage in an optically complex environment. However, there do not yet exist detailed enough reflectance function measurements for marine animals to fully understand their camouflage strategies. Such measurements are difficult to obtain and require specialized instrumentation, since it is necessary to control the illumination and viewing conditions during acquisition. To this end, we report the design and initial results for an optical instrument constructed to record the BRDF of marine organisms in the field.

2. Instrument for measuring angular reflectance

2.1. Design considerations

The use of scatterometers for measuring the BRDF of small biological samples has yielded promising results [11, 12], and indicate that such methods can be successfully applied in coloration investigations. The main drawback to the approach used in these studies, is that placement of samples at the focal point of an ellipsoidal mirror obstructs the light path, limiting captured light at near normal angles, even for small samples. Therefore, an instrument with an ellipsoidal mirror as the primary imaging optic is not suitable for measuring marine organisms collected in the field, which are found in a wide range of sizes.

For marine organisms, the acquisition speed must be high enough such that the samples do not deteriorate significantly during measurement. A time limit of ∼ 20 minutes for complete measurement is reasonable to ensure sufficient tissue hydration. One potential solution is found by using light emitting diodes (LEDs), which can be modulated very quickly using high speed A/D converters, enabling dense BRDF measurements in seconds. LEDs were used in the fiber-based instrument for measuring marine surfaces of [13], the LED-only hemispherical system of [14], and the handheld condenser reflectometer system of [15]. Projector based systems, such as that in [16], offer another option for high speed BRDF measurement. Compared to a light source consisting of multiple collimated LEDs, a digital projector is a much simpler solution, since the incident illumination angles can be selected by displaying a series of images of varying patterns.

In addition to high acquisition rates, when properly selected, both of these source types can enable spectral measurements. LEDs are manufactured for a wide variety of wavelengths, whereas projectors are available with three discrete (red, green, and blue) wavelengths, provided by individual LEDs or laser diodes. Here, the ability to perform spectral measurements would be useful when considering the data in an ecological context.

2.2. Hardware design

The optical scatterometer for measurement of angular reflectance (OSMAR) is shown in Fig. 2. A key design choice was the selection of the source as a small digital projector containing three laser diodes. Combined with a high numerical aperture objective lens and the placement of a pinhole aperture in front of the camera lens, the projector enables rapid BRDF measurement of small points on a sample of arbitrary size, at three discrete wavelengths. Full component specifications are given below.

 

Fig. 2 System layout and design schematic of optical scatterometer for measurement of angular reflectance (OSMAR). Projector light source S produces a beam at a particular angle that is collimated by lens L₁. The beam is reflected by beamsplitter B onto objective lens L₂ and focused to its back focal point at the location of sample M. The beam simultaneously transmitted by beamsplitter B is focused by lens L₃ onto the collection aperture of power meter P. Light scattered from sample M is collected by lens L₂, transmitted by beamsplitter B, and focused by lens L₄ onto the pinhole aperture A. The light not blocked by pinhole aperture A is collected by lens L₅ and directed with normal incidence onto the sensor of camera C. The process is repeated for all desired incident angles.

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To begin a measurement, the sample M is placed on a three-axis positioning stage near the focal point of objective lens L₂. The projector S produces a bright positioning spot to be used for sample alignment at a single wavelength. The projected image is collimated by lens L₁, which is placed at one focal length from the origination point of the projector beam, redirected by beamsplitter cube B, and focused by lens L₂. The focused positioning beam is then used as a reference to change the lateral position of sample M by adjusting the positioning stage, which allows for precise selection of the desired sampling point. While viewing the live camera image, the sample M is moved along the optical axis to the focal point of lens L₂ by adjusting the axial micrometer on the positioning stage. The sample area is then covered with a black light curtain to minimize incident ambient light. The system is then ready to collect measurements for a single wavelength.

The projector S displays a set of binary images that illuminates the sample from angles determined by the selected pixel regions. For each image, a narrow beam of light is collimated by lens L₁ and directed onto the beamsplitter cube B. The light is reflected by the beamsplitter cube B and focused by lens L₂ onto the sample M. Simultaneously, the light that is transmitted by beamsplitter cube B is focused by lens L₃ and captured by power meter P, connected to an integrating sphere with the opening placed just in front of the focal point of lens L₃. The power readings are later used to normalize the data to compensate for fluctuations of the light source.

Light that is reflected from sample M within the field of view of lens L₂ is collimated and directed to beamsplitter cube B. The transmitted light is focused to the polychromatic minimum blur spot of the achromatic focusing lens L₄, which is collocated with pinhole aperture A. The pinhole aperture A eliminates light from off-axis sample points, and out of focus reflections that may confound the captured image. After passing through pinhole aperture A, the light is then collimated by the achromatic imaging lens L₅, and directed with normal incidence onto the CCD of camera C. For each binary image displayed by projector S, a corresponding image is captured by camera C via software trigger. After all patterns have been projected and images captured, the process is restarted for the next wavelength. A typical measurement set utilizes all three wavelengths of the light source.

The following is a list of components with associated specifications used in the OSMAR system described above. The light source S is a pico projector development kit (MicroVision, Inc., Redmond, WA). The projector comes in a small package (50 mm × 46.5 mm × 7.6 mm without heatsink), provides a resolution of up to 848 × 480 (limited here to 480 × 480), has a high contrast ratio of 5000:1, a 60 Hz refresh rate, and the lasers have wavelengths 640±1.4 nm (red), 532 ± 1.2 nm (green), and 450 ± 1.4 nm (blue), with measured power of $~10\frac{\text{nW}}{\text{pixel}}$. The position of projector S is adjusted using a ThorLabs GNL10 goniometer with ±10° adjustment and ThorLabs XYR1 linear translation and rotation stage. The collimating lens L₁ is a ThorLabs AL50100-A 50 mm f/2 aspheric lens.

The lenses L₂ and L₃ are identical Edmund Optics NT67-255 50 mm f / .6 aspheric lenses, that yield an angular field of view of ∼ 45° half angle and a chromatic focal shift of 1.02 mm over the wavelength range used. Lenses L₄ and L₅ are Edmund Optics NT49-284 50 mm f / 2 and NT49-313 9 mm f / 1.3 achromatic doublets respectively. The beamsplitter B is an Edmund Optics NT49-004 50 mm 45R/45T non-polarizing beamsplitter cube. The power meter P consists of a ThorLabs PM100USB controller and S142C integrating sphere. The aperture A is an Edmund Optics 100 μm NT36-392 pinhole. The camera C is an Allied Vision Technologies GC1380 2/3” format CCD 12-bit GigE camera with 1360 × 1024 resolution, 6.45 μm × 6.45 μm pixel size, and frame rates up to 20 fps. The optics and camera are mounted in the ThorLabs lens tube system, with a custom-fabricated beamsplitter cube holder, and are secured to a ThorLabs DP14 dynamically damped post. The entire system assembly is mounted on a ThorLabs PBG11101 ultralight breadboard placed above 6.5 mm thick Sorbathane sheet for additional vibration damping, which is necessary for measurements taken aboard research vessels.

2.3. Software design

The illumination is provided by projecting binary images generated using a custom MATLAB (The MathWorks, Inc., Natick, MA) program. After obtaining the mapping between projector image pixel position (x_p, y_p) and sample incident angle (θ_i, φ_i), as described below, it is straight-forward to select the desired angle by setting the corresponding pixel value to 1 (instead of 0) in a binary image. A projected image will then illuminate the sample surface from the angles indicated by the enabled pixels in that image. Typically, a single image corresponds to a single incident angle selection, although arbitrary patterns may be created based on the measurement requirements.

A series of images is displayed by connecting the projector to the video port of a laptop computer. A custom Quartz Composer (Apple, Inc., Cupertino, CA) program is then used to cycle through the images. The program also allows for adjustment of source power level, although stability is compromised if the value is set too low. After an image is displayed and held for the specified amount of time, a software trigger directs the camera to capture a reflection map. The camera is controlled by a custom C++ program, which provides a simple method of modifying integration time, gain settings, and other useful acquisition parameters.

2.4. System calibrations

Geometric calibration is necessary in order to obtain a mapping between projector pixel position (x_p, y_p) and incident angle (θ_i, φ_i), and the camera pixel position (x_c, y_c) and viewing angle (θ_o, φ_o). The first step towards determining these mappings is to enable optical distortion correction of the recorded images. The standard method of camera calibration [17] uses images of a checkerboard captured under multiple orientations. Grid corner positions are extracted from the images and, based on the known geometry of the physical grid, the locations of undistorted corners are calculated. A similar technique is performed here, but instead using a custom fabricated pinhole occluder. When placed in front of the objective lens with a diffuse reflector in the sample position, a large diameter beam is sent through the system at each of the three wavelengths. Distorted images of the pinhole occluder captured for multiple rotations about the optical axis are analogous to those of the checkerboards. Figure 3(a) shows an example image for a single occluder rotation. The centroids of each pinhole subimage are compared to the known positions on the occluder and the camera calibration matrix is estimated. This matrix can then be used to undistort arbitrary images captured using the corresponding wavelength.

 

Fig. 3 Example pinhole occluder images used for geometric camera calibration and viewing angle mapping estimation. (a) Original image. (b) Undistorted image.

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Using the undistorted pinhole occluder images, as shown in Fig. 3(b), the camera CCD pixel position (x_c, y_c) to viewing angle (θ_o, φ_o) mapping can be determined. The distance z_PS from the pinhole occluder and sample is measured, and the position (x_c0, y_c0) of the optical axis is found during the camera calibration procedure. The pinhole centroid positions (x_PC, y_PC) relative to the optical axis are calculated and converted to metric units using the CCD dimensions. The zenith viewing angle for a single pinhole centroid, with x_PC = 0, is calculated as

The projector image pixel position (x_p, y_p) to incident angle (θ_i, φ_i) mapping is determined using a mirror as the sample target and analyzing undistorted images captured from single pixel or pattern projected images. The incident and viewing angles have the relationship (θ_i = θ_o, φ_i = φ_o ± 180°) due to specular reflection about the normal, so the pixel position to incident angle correspondence is determined using the previously calculated viewing angle mapping. The full mapping of projector pixel positions to angles for the system is then completely known.

In summary, the path of incident and reflected light rays as they travel through the system, when a mirror is used as the target sample, is as follows. A projector pixel (x_p, y_p) is enabled and produces a ray with origin at the focal point of lens L₁. The ray is collimated by the lens and proceeds to beamsplitter cube B, where it is reflected by 90° about the original optical axis and is then incident on objective lens L₂. The ray is focused by the lens to its back focal point at M with incident angle (θ_i, φ_i). A reflected ray leaves point M with outgoing angle (θ_o, φ_o) and is collimated by lens L₂. It passes through the beamsplitter and is incident on lens L₄, where the lens focuses the ray to its back focal point at A. The remaining light that is not blocked by the pinhole aperture A proceeds to the lens L₅ where it is collimated and relayed to camera C to the particular pixel (x_c, y_c), or region of pixels, corresponding to (θ_o, φ_o).

Radiometric calibration is also required to take into account nonlinearities in camera response as a function of scene irradiance. Due to the system illumination characteristics and geometry, it is not possible to use color chart methods to recover the inverse camera response function, i.e. the mapping between scene irradiance and camera CCD pixel intensity. Recovery of this function thus followed the intensity mapping function procedure using the cumulative histogram method [18]. Eight images of a single sample were captured, with exposure times ranging from 17 ms to 136 ms, at multiples of 17 ms. Except for some indication of nonlinearity at intensity levels near saturation, the camera CCD response was estimated to be highly linear. Therefore, special care was taken to ensure that captured images did not approach saturation.

Due to the low power per projected (incident) pixel of ∼ 10 nW, larger regions of 15 × 15 pixels were selected, subtending an average angle of 2.2°. Although the power meter is used to monitor the source with an equivalent view to that of the object, the size of the incident illumination beam on the object is larger than that seen by the camera. That is, the image of the pinhole aperture on the object plane is approximately 20 μm diameter, which is slightly smaller than the illumination beam size measured using a CCD camera placed at the same plane. Therefore, the power meter is used to compare relative fluctuations in source levels, but these values are not considered to be absolute.

Angular resolution of the recorded reflection maps was estimated at an average of approximately 0.13 degrees per pixel, or 7.9 pixels per degree, with resolution decreasing at higher viewing angles due to spherical aberration and geometric effects. The maximum dynamic range of a single captured image is approximately 70.5 dB (11.7-bit), as measured using an aluminum mirror with a BRDF on the order of 10³ sr⁻¹. The overall dynamic range of the system, defined here as the log ratio of maximum to minimum measurable BRDF value, can be increased by using multiple exposure methods. This technique results in a maximum system dynamic range of 104 dB (17.2-bit). Although it is possible to use the system to measure extremely high (aluminum mirror) or low (black diffuse standard) BRDF values, most of the marine specimen BRDFs obtained so far are on the order of 10⁰ or 10¹ sr⁻¹. However, multiple exposure methods were still used since it is preferable to keep source power level as high as possible. Note that the reported values correspond to the green wavelength (λ = 532 nm), but values for the other wavelengths are similar.

2.5. BRDF acquisition

The acquisition of sample BRDF is as follows. A set of illumination patterns, representing selected incident angles, is projected through the system and the reflected light is captured by the camera. These images are processed by a set of custom MATLAB programs with the following steps: subtraction of dark frame image, intensity gain response correction if required, undistortion of images using determined camera calibration matrix, normalization of values by integration time for ease of sample comparison and prevention of large values, normalization of values by measured power reading, and calculation of BRDF. The reference method for BRDF calculation [19, 20] uses the simple relationship

After processing the images as described above, the BRDF map is calculated for all measured incident angles by dividing each sample reflection map by the corresponding reference reflection map of the gray Spectralon (Labsphere, Inc., North Sutton, NH) reflectance standard DRS-40, and multiplying by the reference BRDF map. The DRS-40 is assumed to be a perfectly diffuse reflector, with a BRDF value of $\frac{.40}{\pi }$ for all viewing angles.

In general, it is possible to use any material as a reference as long as it has a known BRDF. A set of eight reflectance standards ranging from DRS-02 (black) to DRS-99 (white) were tested as potential references. Using the above procedure, each standard was individually selected as a reference, and the BRDF values for the remaining standards were estimated. The lower range of reflectance standards allowed for computation of BRDF for all others, except for those with reflectance higher than the DSR-40 standard. Deviations at these high reflectance values were assumed to be due to surface roughness, as the spatial resolution of the system viewing area is smaller than the particles used to produce the large scale rough appearance of Spectralon. Therefore, caution should be exercised when considering these materials as reference standards in scatterometers with small viewing areas.

Reflection maps are captured using a software trigger, which limits the acquisition rate to ∼ 5 frames per second. In the current configuration, 169 different incident illumination angles are selected. A dark frame is also captured before each measurement, yielding a total of 338 frames for a single data set. For a single point on a given sample, a measurement is made at each of the three available wavelengths, resulting in an acquisition time of less than 3.5 minutes, which is well under the imposed measurement time limit of 20 minutes. Therefore, it was possible to obtain reflectance functions for multiple points on a single sample, as well as record multiple exposures of each point.

3. Results

3.1. Field study

A field study using the OSMAR system was performed during a research cruise on the R/V Kilo Moana near the Hawaiian islands from May 29 to June 9, 2012. Specimens were caught using a Tucker trawl net with a three square meter opening. The net provides electronic control of the opening and closing mechanism and directs the captured water parcel, including organisms, into an insulated, closing cod end which allows for preservation of animals from deep ocean waters. This type of net is particularly useful for obtaining fragile soft-bodied organisms, such as cephalopods.

The two primary animals of interest are shown in Fig. 4. The deep sea squid Pterygioteuthis microlampas has a maximum mantle length of 34 mm [21] and the silvered fish Sternoptyx sp. has a maximum length of 60 mm [22]. The animals presented here were caught at ∼ 300 m depth. Following recovery of the trawl net, all specimens remained immersed in seawater until beginning preparation for measurement. P. microlampas specimens (example shown in Fig. 4(a)) were sacrificed by quick decapitation, and mantle skin sections were dissected and pinned onto a Sylgard dish. Sternoptyx sp. specimens (example shown in Fig. 4(b)) were deceased due to barotrauma prior to arrival at the surface and were measured whole. Water was drawn off the sample and all reflectance function measurements were completed within 20 minutes to ensure tissue hydration.

 

Fig. 4 The animals of interest. (a) Pterygioteuthis microlampas. (b) Sternoptyx sp. Scale bars are approximately 10 mm.

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3.2. Scattering patterns and BRDF values for P. microlampas and Sternoptyx sp.

A typical example of a reflectance function measurement for the squid P. microlampas is shown in Fig. 5. For this specimen, the BRDF was measured at two lateral points, one on either side of the dorsal line of the body, as indicated by the blue and red dots in Fig. 5(a). The BRDF scanline plots in Fig. 5(b) show a broad specular peak surrounded by diffuse reflectance, with some retroreflection also present. Note that the scanlines do not go exactly through θ_o = 0°, as seen in the BRDF maps, since the estimation of incident angle is based on system calibrations performed using a flat mirror, which indicates that the specimen surface itself is not perpendicular to the optical axis. Effectively, this changes the inclination of the incident angle and normal estimation can be performed to correct for the deviation.

 

Fig. 5 Directional reflectance of Pterygioteuthis microlampas mantle skin measured at λ = 532 nm. (a) Dissected mantle tissue with measurement points indicated. (b) In-illumination-plane BRDF line scans. (c) BRDF map for left lateral (blue) point. (d) BRDF map for right lateral (red) point. The BRDF maps show the BRDF for each measured point from θ_o = 0 to 45° and φ_o = 0 to 360° for the incident illumination angle indicated by the white asterisk. Each green circle represents an increment of the angle θ_o by 15°. The pink asterisk indicates the estimated specular point. In-illumination-plane scanlines are marked by blue and red dashed lines.

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The scattering patterns shown in Figs. 5(c) and 5(d) indicate that the reflected light is predominantly scattered into a highly limited range of angles and decreases away from the specularity. Patterns corresponding to other incident illumination angles (not shown) also exhibit similar behavior, including preservation of the angular fan orientation. The presented BRDF maps were contrast enhanced to improve visibility of the lower value regions in a single image. However, the actual data does not exhibit saturation, as it was possible to capture images using multiple exposure values for each measurement point. Measurements were also performed at the remaining two system wavelengths. That data is not presented here, but the general appearance of the scattering pattern is similar to what is shown.

A representative reflectance function measurement from the silvered fish Sternoptyx sp. is shown in Fig. 6. For this specimen, the BRDF was also measured at two points, one near the head and one near the tail, as indicated in Fig. 6(a). The BRDF scan line plots in Fig. 6(b) show multiple specular peaks surrounded by diffuse reflectance, as well as some retroflection. The scanline deviation from normal is quite apparent for the tail point, and is expected due to the higher curvature on that area of the body. Scattering patterns shown in Figs. 6(c) and 6(d) are similar to that of P. microlampas in that they are restricted to a small range of angles, with unchanging orientation regardless of incident angle. The primary difference between the BRDF of the two species is the presence of multiple specularities for Sternoptyx sp. Again, reflectance function data for the two additional system wavelengths is similar to that presented.

 

Fig. 6 Directional reflectance of Sternoptyx sp. scales measured at λ = 532 nm. (a) Whole fish with measurement points indicated. (b) In-illumination-plane BRDF line scans. (c) BRDF map for head (blue) point. (d) BRDF map for tail (red) point. The BRDF maps show the BRDF for each measured point from θ_o = 0 to 45° and φ_o = 0 to 360° for the incident illumination angle indicated by the white asterisk. Each green circle represents an increment of the angle θ_o by 15°. The pink asterisk indicates the estimated specular point. In-illumination-plane scanlines are marked by blue and red dashed lines.

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4. Discussion

A unique instrument has been developed for measuring the directional reflectance functions of marine organisms. The OSMAR system is portable and provides fast data acquisition at discrete wavelengths. The optical design is similar to the hand-held condenser reflectometer system of [15] and the modified epi-illumination microscope of [23]. However, the first case uses a small number of fixed white LEDs as the light source and the second case uses mechanical diaphragms to control the illumination angle. The laser projector source in the current system allows for simple selection of incident angle, beam size, and intensity at three wavelengths. Simultaneous monitoring of relative source power levels is an additional key feature of the instrument. The use of an adjustable sample stage allows for precise positioning and measurement of small samples.

There are some improvements that could be made to the current system. Having a continuous magnified view of the sample would be useful during placement for acquisition as well as for comparing the processed data within and between samples. This could be accomplished by adding another beamsplitter in between the current one and the pinhole and camera assembly, to direct the image to another camera with a standard lens attached. Replacing the objective with a well-corrected lens would eliminate the need for translation of the sample stage between measurements at different wavelengths, improving consistency. However, one begins to approach microscope objectives if numerical aperture is to remain high and with this comes minuscule working distances and extremely shallow depth of field. The issue of spatial scale also becomes increasingly important as viewing area decreases. The size of the structures under study will dictate these limits and must be taken into consideration if accuracy of the measured BRDF values is to be maintained.

An enlarged stereo microscope image of P. microlampas mantle tissue is shown in Fig. 7. It is apparent that the highly reflective surface consists of several parallel ridge-like structures. Relative to the body of the animal, these structures are oriented along the longitudinal axis. The BRDF maps presented in Fig. 5 indicate that light is primarily scattered perpendicular to these structures. Reflection of the pattern orientation over the dorsal line of the animal provides further evidence for this claim. The BRDF maps for Sternoptyx sp. in Fig. 6 show that the orientation of the patterns is perpendicular to the arrangement of scales on the body of the fish. The observed patterns also indicate reflection that is more specular than diffuse. In addition, peak BRDF magnitude values are approximately twice those of P. microlampas.

 

Fig. 7 Microscope image of P. microlampas mantle enlarged to show detail. Scale bar is approximately 1 mm.

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Since the tissue samples were not dehydrated, it seems reasonable to assume that there must be some component of the observed reflection due to an extremely thin layer of water remaining on the surface. However, we have confirmed that in this system, a thin layer of water above a variety of tested materials primarily contributes to the reflection as an increase in the specular peak. That is, the underlying appearance of the material is preserved. Further analysis of the full data set will involve estimation of the contribution of the water layer to the measured BRDF maps.

The two species described here are evolutionarily diverse but inhabit similar environments, so it is interesting that they exhibit such strikingly similar, possibly convergent directional reflectance properties. A reasonable assumption may be that such patterns provide evidence of a single camouflage strategy. Another intriguing connection may be to the Morpho aega butterfly. Scattering patterns from the dorsal wing scales of this species have been previously reported [12] and appear to be quite similar to those described here, in that incident light is predominantly scattered perpendicular to surface ridges. Although the structure of Morpho spp. tissue has been well studied [23], without similar information for P. microlampas and Sternoptyx sp., it is not possible to compare the physical scattering mechanisms of these species.

Some preliminary work toward obtaining the BRDF of skin from the squid Loligo pealeii was outlined in [24], but no numerical values were given. Spectral reflectance and transmittance data for chromatophores and iridophores from the same squid species was presented in [25], and even included limited directional information, although for only three angles of incidence and one viewing angle. The appearance of mirrored fishes has also been well described [2,3,26]. However, to our knowledge, the data presented here are the first detailed BRDF measurements for any marine species, and demonstrate that light scatter from these animals is more complex than that of a simple mirror.

In this article we considered only a limited data set from our field study. In addition, no physical model for the observed scattering patterns has been proposed. In future work, we plan to perform a comprehensive analysis of the complete measurement sets for the two described species, as well as others collected during the research cruise. Optical scattering models will then be devised to explain the reflectance functions of P. microlampas and Sternoptyx sp., using information gathered from electron microscopy. This additional work is underway.