Transmission through muscle tissue shapes polarization signals during cuttlefish courtship

Significance

Many animal tissues (e.g., muscle fibers and collagen) are translucent yet exhibit rich optical properties such as scattering and diffraction. In this study, we show that transparent muscle tissue in cuttlefish can actively shape visual signals for courtship by modulating light polarization—the orientation of light wave oscillation. Using photopolarimetry, we reveal that sexually ornamented cuttlefish arms display a spatial pattern of horizontal and vertical polarization. This enhances visual contrast optimally for cuttlefish polarization vision. The pattern arises from light transmission across a birefringent muscle layer that rotates the angle of polarization. Our findings uncover a hidden optical function of transparent muscle and suggest that polarization signals, like color, can evolve for conspicuousness and efficacy.

Abstract

Flamboyant sexual ornaments serve as conspicuous visual signals optimized to the visual receptors and perception of potential mates. While numerous studies have explored the mechanisms and functions of body coloration as a sexual signal, the role of another essential property of light—polarization—remains largely unexplored. Specifically, the question of whether and how polarization signals achieve high conspicuousness under sexual selection, including their visibility and associated behavioral and morphological adaptations, has yet to be thoroughly investigated. Here, we identified a strikingly conspicuous polarization signal used specifically during courtship in the cuttlefish Doratosepion andreanum and investigated the underlying optical mechanism. The signal consists of a pattern of adjacent horizontally and vertically polarized areas, optimizing signal detectability for cephalopod polarization vision. This pattern is generated by reflective cells called iridophores and transparent muscle: light becomes horizontally polarized when reflected by iridophores, and its angle of polarization is then rotated to vertical when transmitted through a birefringent muscle layer. Our findings show the significant contribution of polarization of light to animal communication and reveal that polarization signals—like colorful sexual ornaments—can achieve high conspicuousness through fundamentally different optical mechanisms.

Sexual signals must attract attention if they are to be effective in mate selection by visual appeal and therefore need to be conspicuous (1). Selection may therefore favor signals maximizing their detectability for the intended receiver’s visual system in a particular environment (2, 3). This can result in males with extraordinary ornamentation and flamboyant coloration such as the peacock’s iridescent feathers with conspicuous eyespots (4). While such sexual signals have been explored primarily for their properties of color (wavelength of light), some animals utilize a different property of light to transmit visual information: polarization. Alongside color and intensity, polarization is a third physical property of light referring to the orientation of light wave’s oscillation. Humans cannot perceive the polarization of light but many other animal groups can, such as insects, crustaceans, and cephalopods (5). Polarization vision in these animals has similarities with color vision, and can be used to obtain visual information to aid in functions such as navigation (6), target detection (7), or visual noise reduction (8). Additionally, some species possess body surface areas that reflect strongly polarized light, which probably serve as a visual signal (9–11). It is therefore predictable that sexual selection would shape extraordinarily conspicuous polarization patterns used for reproductive communication in animals with polarization vision, like a colorful ornamentation in animals with color vision. However, whether and how this conspicuousness is achieved remains unknown.

Here, using the cuttlefish species Doratosepion andreanum, we identified courtship polarization signals produced by a pair of sexually ornamented arms which are considered to render these arms distinctively conspicuous to animals such as cephalopods possessing polarization vision. Most animal polarization patterns are produced by structural reflection at the body surface and such reflected light is polarized only in the horizontal direction (12), but we found that this particular courtship polarization pattern is produced by a different optical mechanism, combining reflection and transmission through the transparent body itself, causing birefringence and creating unusual, vertically polarized light, which contrasts maximally against the background of horizontally polarized light.

Results

Male Exhibits Polarization Signals Specialized for Courtship Display.

Males of the cuttlefish D. andreanum have two sexually dimorphic arms (SDAs) approximately three times longer than the equivalent arms of females (Fig. 1A). These SDAs are usually rolled up in front of the head. During courtship, however, when the male extends his body and turns the body color pale, he also extends the SDAs, which display iridescent banding patterns (Fig. 1 B and C). After performing this display for several seconds, the courted female indicates her acceptance by opening her arms, after which mating occurs (13). Since polarization patterns on cephalopod body surfaces are changeable through morphological changes in reflective cells called iridophores and the more superficial chromatophores (14–16), these SDAs may show a special polarization pattern during the courtship display.

Fig. 1.

Polarization courtship display of Doratosepion andreanum. (A) Sexually dimorphic arms (SDAs) in D. andreanum. Counting from the dorsal midline, the second pair of arms of the male is very much longer and stouter than the other arms. (B and C) Schematic illustration of courtship behavior in D. andreanum. (B), Usually, the male’s SDAs are retracted, coiled together with the other arms, but (C) at the moment of courtship display, they are extended, and a pattern of iridescent bands appears on them. (D) Diagram illustrating the polarization parameters of light, DoLP (degree of linear polarization) and AoLP (angle of linear polarization). The color bars represent corresponding false color maps used in the following figures showing the results of photopolarimetry: DoLP is represented as intensity and AoLP as hue. (E and F) Photopolarimetry of lateral views of D. andreanum where courtship is not taking place. Top: normal RGB images in which intensity has been enhanced for better contrast. Bottom: False color images. Note the color map in the Bottom Right corner. (E), Female. (F), Male. The white arrow indicates male SDA. (G) Continuous photopolarimetry of the courtship display by the male, taken at 0 s (Left), 0.14 s (Middle), and 0.48 s (Right). (H) Enlarged image of Right panel of (G). Square: bright region of the Right SDA. Circle: tip of Left SDA. Diamond: tip of Right SDA. (I) AoLP and DoLP of SDA during courtship display (n = 5). Angles represent AoLP and the distance from the center represents DoLP. Gray scale profile represents the 2D kernel density estimate in the SDA area normalized by the maximum density, where light gray denotes high distribution. Points represent the means of specific parts of the SDA, corresponding to those indicated in (H). Error bars indicate SD.

In a captive environment with intensity artifacts of light carefully removed, we first took photopolarimetry images of D. andreanum in several situations using a camera equipped with a polarized sensor (polarization camera) (17). From these images, the degree of linear polarization (DoLP, the proportion of light oscillating in a specific plane) and the angle of linear polarization (AoLP, the mean direction of the oscillation) (Fig. 1D) were calculated for each pixel, and polarimetry images showing DoLP and AoLP as false intensity and color, respectively, were produced. In the absence of a courtship, male arms including SDAs and also the arms of females show plain horizontally polarized stripes (Fig. 1 E and F), which is a common feature among cuttlefish species (15, 18). However, during courtship, from the courted female’s perspective, a dynamic pattern of strongly polarized bands appears on the SDAs of the courting male (Fig. 1G and SI Appendix Movie S1). This unique polarization pattern was composed of horizontally and vertically polarized light (Fig. 1 H and I). The SDA nearer to the female shows vertically polarized bands pattern. At the rounded tips of the SDA, AoLP is orthogonally different between the two SDAs, with the tip of nearer SDA showing vertical polarization while the tip of further SDA, presented to the female by twisting, shows horizontal polarization.

The Courtship Polarization Pattern Is Highly Conspicuous to Cuttlefish Polarization Vision.

Cephalopods including cuttlefish possess diplotic polarization vision, analogous to dichromatic color vision, based on two photoreceptor channels sensitive to horizontally and vertically polarized light relative to the horizontal seabed (19, 20). Based on this mechanism, previous studies have proposed a neurophysical model termed Polarization Distance (PD) to evaluate polarization contrast between two objects (21). In this model, the opponency signal between these two channels is indicated as P₁. PD is calculated as the comparison of two P₁, one viewing object a (P_1,a) and one viewing object b (P_1,b), given by

$$\mathrm{PD}=\frac{\left|P_{1,\mathrm{a}}-P_{1,\mathrm{b}}\right|}{2\left(ln10\right)}.$$

The maximum polarization contrast, analogous to complementary colors for color vision, is achieved by the combination of lights fully linearly polarized horizontally and vertically (Fig. 2A) (See Materials and Methods for more detailed explanation of the model).

Fig. 2.

SDAs during the courtship display are conspicuous to cephalopod polarization vision. (A) False-color map of normalized P₁ activity (P’₁) corresponding to AoLP and DoLP. Vertically polarized light induces excitatory responses (blue), while horizontally polarized light induces inhibitory responses (yellow). (B) False-color map representing P’₁ produced from photopolarimetry of a female (Top Left) and a male in the absence of any sexual encounter (no courtship, NC) (Top Right) and during a courtship display (CD) (Bottom). Inset at higher magnification shows the tips of the two SDAs of a male. Areas enclosed by white lines indicate regions of the image where the arms are located. Gray circle, diamond, and square represent nearest tip, furthest tip, and middle area, respectively, of the SDA during the courtship display. (C) Distribution probability of P’₁ in the enclosed arms region [females, n = 6; males (NC), n = 7; males (CD), n = 5]. Bar width corresponds to the threshold of cuttlefish polarization vision (PD = 0.013) (22, 23). Gray bars indicate the possible range of P’₁ induced by the expected degree of polarization in the habitat background (24, 25). In the histogram for males (CD), the plots and error bars represent mean ± SD of the P’₁ in each area [shapes correspond to those in (B)]. Double-headed arrows illustrate the PD of the middle area of the SDA against the background (Left) and the PD within the SDA tips (Right). (D) PD of entire arm region against estimated background polarization (mean ± SD). Stats represent P < 0.05 (Kruskal–Wallis test followed by Dunn’s test with Bonferroni correction). Dashed line [in (E) also] represents the threshold of cuttlefish polarization vision. (E) SD of P’₁ among proximal and tip regions of the arms (mean ± SD). Stars represent P < 0.05 (Kruskal–Wallis test followed by Dunn’s test with Bonferroni correction). Note that threshold of cuttlefish polarization vision applied here has been obtained with other cuttlefish species.

Conspicuousness of visual signals can be measured as contrasts with the visual background or within the body pattern (26, 27). From the photopolarimetry images, we calculated the normalized P₁ (P’₁ = $\frac{P_1}{2\left(\mathrm{l}\mathrm{n}10\right)}$) for each pixel and represented it on a pseudocolor map (Fig. 2B). This revealed that SDA provides strong P₁ both in the positive and negative direction during the courtship display. The PD between the entire arm region versus the estimated polarization background of the natural habitat of this species (24, 25) was well above the threshold of the ability of the cuttlefish eye to detect PD (note that this threshold was determined in other cuttlefish species) (22, 23), and significantly greater compared to those of both males and females in a noncourtship situation (Fig. 2 C and D). Furthermore, the SD of P’₁ was also higher in the courtship display, indicating strong polarization contrast within their SDAs (Fig. 2E). In particular, the two SDA tips, placed together, produce a very marked PD (Fig. 2C), reminiscent of an adjacent maximally contrasted chromatic pattern in sexual ornaments in other animals (28, 29). These results demonstrate that the male’s courtship display is highly conspicuous due to strong polarization contrast, both against the background and within the pattern.

Vertical Polarization Is an Unusual Phenomenon in Nature.

While strong polarization, especially vertical polarization on the SDA creates marked conspicuousness, it is noted that the combination of a reflection strongly polarized in a contrasting orientation is an unlikely phenomenon in nature, not reported for the body surface of other animals. Considering Fresnel’s equation, the light component polarized perpendicular to the plane of incidence (s-waves) reflects more than the component polarized parallel to the plane of incidence (P-waves) (SI Appendix, Text and Fig. S1). Therefore, when natural light arrives from overhead, light reflected from a horizontally oriented animal body surface will inevitably become horizontally polarized, corresponding to s-polarized light. As a result of this optical constraint, all polarization signals described previously are mostly horizontally polarized in the normal viewing condition (12). Therefore, the vertically polarized reflection in the SDA challenges this convention, indicating the likelihood of a distinct mechanism within the SDA responsible for the observed presence of vertical polarization.

The Arms of the Male Have Acquired a Novel Morphological Feature in Their Iridophores.

Polarization patterns of cephalopods are produced by iridophores in the dermis, composed of stacks of protein platelets (15). The distribution and morphology of iridophores provides a hint to explain the mechanism of complex polarization patterns on the male SDA. Therefore, transverse sections of the male SDA and the corresponding arm of the female were examined (Fig. 3A) using both the light microscope (LM) and transmission electron microscope (TEM).

Fig. 3.

Sexual dimorphism of iridophore morphology and distribution. (A) Top: Schematics of transverse sections across all the arms of a female and a male D. andreanum. The arms colored blue (Left SDA) are those from which histological sections were taken. The black line and arrow indicate the plane of section and an oral view below, showing the positions and orientation of the target arm. The mouth (M) is at the center of the arms. Eight arms encircle the mouth (the tentacles are not included), each with the oral side bearing suckers oriented toward the mouth. D, dorsal; V, ventral side. The Left SDA is colored blue. (B–D) Cross-section of the female SDA. (B) LM transverse section. ANC, axial nerve cord; AS, aboral side; Ep, epidermis; M, muscle; OS, oral side; S, sucker. The red area highlights the distribution of iridophores. (C) Higher magnification of the iridophore area in (B). The arrow indicates cluster of iridophores, visible as dark profiles. (D) TEM image of iridophores, showing their multilayered laminar structure. (E–I) Transverse section of the male SDA. (E) LM transverse section. Red highlights distribution of common iridophores; green highlights SDA-specific iridophores. (F) Higher magnification of the common iridophore area in (E) Arrows indicate cluster of common iridophores. (G) Higher magnification of the lateral area near the sucker in (E). Arrows indicate cluster of SDA-specific iridophores. (H) TEM image of common type iridophore. (I) TEM image of SDA-specific iridophore. (J) Schematic of light reflection on the surface of the male SDA during the courtship display. Structures in the box indicate the expected optical path resulting from the distribution of the iridophores and the orientation of their plates. [Scale bar, 500 μm (B and E), 50 μm (C, F, and G), 2 μm (D), 10 μm (H and J).]

A LM transverse section through the female arm (Fig. 3B) shows the presence of dark-stained patches in the epidermis of the aboral side (Fig. 3C and SI Appendix, Fig. S2). TEM imaging confirmed that these are iridophores with a multilaminate structure (Fig. 3D). The non-SDA arm of male also possessed iridophores with a similar shape (SI Appendix, Fig. S3). In contrast, in the male SDA (Fig. 3E), as well as similar dark-stained patches on the aboral side (Fig. 3F), elongated structures with their long axis approximately parallel to the epidermis were observed on the dorsal-lateral side (Fig. 3G and SI Appendix, Fig. S4), and with the TEM these were confirmed to be iridophores. This SDA-specific type of iridophore was morphologically distinct from the common type of iridophore. While the common type has a particular shape and the orientation of laminae varies (Fig. 3H), the SDA-specific type has a uniform slender shape, and its lamellae are positioned almost perpendicular to the iridophore long axis, resulting in their uniform orientation (Fig. 3I). The spatial arrangement of the SDA-specific iridophore parallel to the epidermis renders the orientation of its lamellae roughly perpendicular to the surface. Considering the distribution of SDA-specific iridophores and the orientation of their laminae, light reflected from them is considered to be transmitted through the arm tissue—composed largely of transparent muscle—to reach the courted female during the courtship display (Fig. 3J).

Transmission Through the Arm Creates Vertical Polarization.

Animal muscle tissue is transparent but is known to produce various optical effects (30–32). Based on the findings of the optical path through the arm muscle of D. andreanum, the impact of light transmission through this muscle on its polarization state was investigated. During the courtship display, Fresnel’s equation predicts that the initial AoLP of light reflected from an iridophore is likely to be close to the horizontal direction from the female’s viewpoint. Therefore, first, this situation was reproduced experimentally by preparing a fresh SDA with its skin removed and illuminated with horizontally polarized light using an LED light source and a polarizer (P-A in Fig. 4A). The transmitted light passed through the analyzer (another polarizer, P-B in Fig. 4A) above the tank which can be rotated in 5° increments, and a CMOS camera captured images to measure light intensity for two regions of interest: the arm (ROI_out) and the background (ROI_in) (Fig. 4 A and B and SI Appendix, Fig. S5). The polarization state of the background corresponds to that of the incident light. The P-B angle θ_peak, where the intensity of each ROI reaches its maximum, aligns with the AoLP of each ROI. It was found that not only was the intensity reduced by scattering, but also ROI_out showed a significantly different θ_peak from that of ROI_in, indicating that the AoLP was altered by transmission through the tissue (Fig. 4C). From these intensity variations, AoLP and DoLP of both ROIs were estimated based on Malus’s Law, resulting in the transmission through the SDA altering AoLP markedly from approximately 0° to 90° (Fig. 4D).

Fig. 4.

Birefringence during transmission through the tissues of the male SDA causes AoLP rotation. (A) Experimental setup for measuring the polarization state of light transmitted through the male SDA. The dissected SDA (blue), with skin removed (photo below), was illuminated with polarized light from behind and recorded by camera. The black arrows represent the light path; gray arrows show the AoLP of light. P-A and P-B are polarizers, and θ is the angle of P-B. ROI_in and ROI_out represent two areas where the light directly reaches the camera (ROI_in) and where the light transmits through the arm (ROI_out). (B) Representative images at four angles from a series taken at 5° increments of the P-B angle for one specimen. Red and blue squares indicate ROI_in and ROI_out, respectively. The semicircle indicates the AoLP coordinate. Images are converted to grayscale. (C) Intensity plots of each ROI versus the P-B angle (θ). Red and blue plots represents ROI_in and ROI_out, respectively. Lines: least square fit to Malus’s Law. (D) AoLP and DoLP for ROI_in (red) and ROI_out (blue) (mean ± SD, n = 9). (E) Schematic to explain how complex AoLP patterns form during the courtship display. In the SDA furthest from the female, light from above is reflected at the arm surface and reaches the courted female directly; in the nearest SDA, surface‐reflected light travels through the SDA, rotating the AoLP from horizontal to vertical. (F) Example of changes in ΔAoLP (blue) and DoLP (yellow) during AoLP_in changes. Lines calculated from theoretical variations based on the optical model described in Eqs. 15 and 17.

These results explain how the complex AoLP pattern is produced in the direction of the female during the courtship display (Fig. 4E). In the SDA closest to the female, SDA-specific iridophores reflect light from above toward the interior of the arm. Light reflected from the iridophores is transmitted through the arm, during which the AoLP of the light shifts from horizontal to vertical. The expansion of black chromatophores in banded pattern blocks the transmitted light, producing the bands pattern of vertically polarized light. At the same time, in the SDA furthest from the female, light reflected from common type iridophores reaches the female without transmission through the tissues, so its AoLP remains horizontal. This combination of reflected and transmitted light creates a complex and intense AoLP pattern. We confirmed that vertical polarization produced by light transmission is an SDA-specific phenomenon by comparing the polarization states of the SDA and the corresponding female arm with their skin intact (SI Appendix, Fig. S6). This finding suggests that the location and morphology of the SDA-specific iridophores, which reflect light in the appropriate direction from the distal region, are critical for achieving this mechanism.

Further analyses revealed that this phenomenon is produced by linear and circular birefringence. Linear birefringence (LB) alters the AoLP of transmitted light (AoLP_out) by creating a phase difference between orthogonally linearly polarized light, and circular birefringence (CB) creates a phase difference between left- and right-handed circularly polarized light. Theoretically, the effect of LB varies depending on the AoLP of the incident light (AoLP_in), but the CB effect is independent (SI Appendix, Fig. S7 and S8). Therefore, AoLP_in was varied by rotating P-A, and AoLP alteration (ΔAoLP = AoLP_out - AoLP_in) and DoLP_out were measured. The observed variations were adequately explained using an addition model, which sums the effects of CB, LB, and depolarization caused by scattering (Fig. 4F and SI Appendix, Fig. S9, see Eqs. 14–17 in Materials and Methods for optical model). CB was the dominant contributor to AoLP alteration, accounting for more than 90% of ΔAoLP under conditions simulating the courtship display (AoLP_in = 0°; SI Appendix, Table S1).

Cylindrical Shape of Arm Contributes to Vertical Polarization.

The theoretical ΔAoLP caused by CB is expressed as $\mathrm{\Delta }AoLP=\frac{\mathrm{\Delta }nL\pi }{\lambda }$, where λ is the wavelength, Δn the refractive index difference between right and left circularly polarized light, and L the path length. This relationship implies that the AoLP of transmitted light depends on the optical path—in this case, the width of the SDA. This prediction was supported by measurements of |ΔAoLP| in three SDA areas (Fig. 5A). As the measurement area shifted toward the thinner distal part, |ΔAoLP| also decreased (Fig. 5B). The |ΔAoLP| was closest to 90° in the middle area of the SDA (85.1 ± 13.3°). Our morphological measurements further show that the male SDA is thicker than the corresponding female arm throughout its entire length (Fig. 5C). Considering that the width of middle SDA area (3.80 ± 0.49 mm) is nearly optimum for producing vertical polarization, the male SDA maintains an approximately cylindrical profile that keeps its width close to that of middle area, compared with the typically conical shape of the female arm (Fig. 5C). Overall, this unique morphology of the SDA—thicker and more columnar than the typical arm—likely enables it to generate vertically polarized signals across its entire surface.

Fig. 5.

Cylindrical shape of SDA contributes to producing vertical polarization. (A) Schematic showing the arm areas in males and females. Dotted lines represent the areas where |ΔAoLP| was measured in (B). (B) |ΔAoLP| in three areas of the male SDA. The x-axis corresponds to the arm areas shown in (A). Stars represent significant differences at P < 0.05 (Wilcoxon test, BH-corrected, n = 6). Data shown as mean ± SD. (C) Arm width at each area of arms (n = 61). The x-axis corresponds to the arm areas shown in (A).

Discussion

The present study investigated the polarization pattern of sexually ornamented traits, and identified their extraordinary conspicuousness in tune with the polarization perception and visual environment of this species in its habitat. This is analogous to other animal species with color vision, in which the conspicuous nuptial coloration in males is tuned to the species-specific absorption properties of the photoreceptors. Such tuning exemplifies the sensory drive theory, which posits that signals evolve in response to the sensory systems of receivers (33). While these conspicuous color patterns are generally achieved by absorption (pigmentation) and reflection (structural coloration) (34), the complex polarization pattern observed here is achieved by completely different mechanisms, a combination of reflection and transmission through transparent muscle layers causing birefringence of the light passing through.

The use of the transmission of light through body tissues for signaling also indicates the significant contribution of polarization to animal communication from a novel perspective. Despite the prevalence of polarization vision across animal taxa, the functional significance of polarization signals has not been demonstrated conclusively for many organisms (12). This is largely due to the difficulty of distinguishing signaling value from among other properties of light, specifically intensity and color. The present study, too, has not provided direct evidence. Due to their ritualized courtship behaviors, which include physical interactions (13), it is almost impossible to experimentally manipulate the polarization state of the courtship display, such as by inserting a polarization filter between the male and the female. However, transmission through birefringent muscle tissue sacrifices some light intensity, indirectly indicating the importance of polarization among the properties of light, especially since cephalopods are color blind (35). The occurrence of vertical polarization in specific behavioral contexts further underscores its role as a meaningful signal. This dynamic pattern may be facilitated by the ability of iridophores to switch between transparency and reflection, as demonstrated in rugate Bragg reflectors in the squid mantle (36).

Our findings also indicate a morphological adaptation of SDA for vertically polarized signal. Due to the physical relationship between circular birefringence and optical path length, to produce vertical polarization, the width of the muscle layer should fall within a certain range when the arm is fully extended during the display. The cylindrical shape of the SDA makes it function as an ideal polarization rotator. In contrast, the conical shape of a typical cuttlefish arm may not be adequate, at least in terms of providing a uniform optical path length across its entire surface. Considering that the arms have other tasks (such as use in feeding), the size and shape of the muscle layers are not determined solely by convenience for signaling. This may explain why non-sexually-ornamented arms of other cuttlefish species, also probably used for signaling conspecifics (15), do not apply this signaling mechanism.

The ubiquity of reflective structures and birefringent tissues utilized in polarization signal production, however, suggests that this mechanism may be employed across many species. Given the species diversity of polarization-sensitive animals such as cephalopods and crustaceans, their polarization characteristics have been studied for only a small fraction of species so far. For example, many cuttlefish species in genus Doratosepion show unique sexual ornaments such as arm or fin elongation, although D. andreanum is the only species whose reproductive behavior has been described (13, 37). Just as with the long-recognized and extensively studied diverse selection of animal coloration, there may be a similar diversity of polarization signals among polarization-sensitive animals—signals that remain entirely unknown to us because they are invisible to the human eye. This study sheds light on a part of that hidden diversity.

Materials and Methods

Animals.

Mature D. andreanum Steenstrup, 1875, were collected from an inshore set net (depth around 20 m) off the coast of Tairadate (Aomori, Honshu, Japan) and maintained as described previously (13). All procedures performed in the ethical standards of the University of Tokyo (Approval numbers P20-7 and P21-16).

Photopolarimetry of Animals.

Definition of DoLP and AoLP.

When partially polarized light is observed through a rotating polarizer, its transmitted intensity I can be described as follows, based on Malus’s Law:

$$I=\alpha +\beta {\cos }^2(\theta -\gamma ),$$ [1]

where θ is the transmission axis angle of the polarizer and α, β, and γ are constants (SI Appendix, Fig. S10). Here, degree of linear polarization (DoLP) and angle of linear polarization (AoLP) are defined as

$$DoLP\equiv \frac{I_{\mathit{max}}-I_{\mathit{min}}}{I_{\mathit{max}}+I_{\mathit{min}}}=\frac{\beta }{2\alpha +\beta },$$ [2]

$$AoLP=\gamma .$$ [3]

Behavioral observation set-up.

For polarimetric measurements, cuttlefish were transported from maintenance tanks to an observation tank (180 × 120 × 90 cm) containing filtered recirculating seawater. The observation tank was housed in a dark room to prevent disturbance from light and other visual stimuli from outside, and was lit with a white LED light during “daylight” between 08:00 and 17:00. Polarized light reflected from body surfaces is markedly influenced by the angle of incident light. Most light comes from above in the natural underwater environment, especially at depths exceeding 20 m (38) where D. andreanum lives (37). To mimic this natural condition as closely as possible, we installed a collection of black rectangular cylinders between a sheet of LED light sources and the tank, and plastic boards covering the entire inner surface of the tank walls, leaving a 20 cm window at the bottom of the glass walls for the camera (SI Appendix, Fig. S11A). These modifications created an environment where light of a constant luminance entered the tank mainly from directly above, minimizing sources of oblique light. A polarization camera was positioned in front of the tank with black cloth reducing the possibility of light entering from the front, and minimizing glare and polarization artifacts.

Set-up and capturing protocol for the polarization camera.

A polarization (TRI050S-QC, LUCID Vision Labs, Canada) operated with LPView ver. 1.2.3 (ViewPlus, Japan) was used to capture the polarization reflection from the body surface of the cuttlefish. Details of the mechanism of this polarization-imaging camera are described in a previous study (17, 39). Briefly, each pixel in the CMOS sensor is subdivided into a 2 × 2 array of smaller subpixels, each of which is monolithically integrated with aluminum nanowires that act as dichroic polarizing filters with orientations of 0°, 45°, 90°, and 135°. Light passing through each array is subsequently filtered with an RGB color filter with sensitivity peaks at 610 nm, 540 nm, and 450 nm, respectively, allowing the following polarization calculation for each color channel. The linear Stokes parameters S₀, S₁, and S₂ are determined from intensity metrics at each subpixel (I₀, I₄₅, I₉₀, I₁₃₅) as follows;

$$S_0=I_0+I_{90},$$ [4]

$$S_1=I_0-I_{90},$$ [5]

$$S_2=I_{45}-I_{135}.$$ [6]

Subsequently, AoLP and DoLP were derived as;

$$DoLP=\frac{\sqrt{{S_1}^2+{S_2}^2}}{S_0},$$ [7]

$$AoLP=\frac{1}{2}\arctan \left(\frac{S_2}{S_1}\right).$$ [8]

False-color images representing polarization properties are then produced, including both the integrated image combining all RGB color channels and separate images extracted from each individual RGB color channel.

To minimize intensity artifacts, photopolarimetry must be conducted with care. Based on a previous review (40), the image capture and processing methods were implemented accordingly. The camera was fixed on a tripod to prevent movement during image acquisition. The aperture was fixed at 1.6 and exposure at 47.0 ms. These settings ensure that the area of interest is mostly captured without overexposure or underexposure. Both male and female D. andreanum were recorded in the absence of courtship; and recordings were also made of the male courtship display. Since the polarization properties of the body surface can differ depending on the angle of observation, the polarization camera was positioned along an extended line connecting the male and the female to approximate the female’s perspective as closely as possible (SI Appendix, Fig. S11B). From the captured image, pixels with values in the lower 3% of maximum pixel value were excluded from further processing for construction of false-color polarization images. For subsequent AoLP and DoLP calculations, the subpixel of the green channel was extracted as this most closely represents the spectral sensitivity of cuttlefish photoreceptors (41).

Polarimetry analysis.

From polarization images of the courtship display, areas containing the SDA were selected manually as Regions of Interest (ROIs). Each image was normalized by pixel number and merged for density estimation. A 2D kernel density estimation with normalized weights generated a semicircular grayscale density map. Mean positions of specific SDA regions (middle, nearest tip, furthest tip) were plotted on the map.

Polarization Distance.

Polarization distance applies the color-distance concept and opponent-processing mechanisms of color vision to polarization vision (21). Invertebrate photoreceptors involved in polarization vision are directionally sensitive because the microvilli are aligned in one direction, responding maximally to light polarized in that direction (42). Polarization sensitivity (R) can be described by the following formula (43):

$$R\left(\phi ,d\right)=\left[1+\frac{d\left(S_{\mathrm{p}}-1\right)}{S_{\mathrm{p}}+1}\cos \left(2\phi -2{\phi }_{\max }\right)\right].$$ [9]

Here, φ is the e-vector axis of light, referred to as the AoLP, and d corresponds to the degree of polarization, DoLP. φ_max is the orientation at which the photoreceptor sensitivity peaks; and S_p is the level of effective polarization sensitivity calculated as the maximum divided by minimum response potential of each photoreceptor. In this study, S_p was set to 10 according to the results from a previous study with cephalopod species (22). Cephalopods have two-dimensional polarization vision, composed of two photoreceptor channels, R_h and R_v, adjusted to horizontal and vertical polarization, respectively, relative to the outside world (20). The signal from these two channels is then compared in a hypothetical interneuron P₁ in the optic lobe with a receptor potential approximated by the natural log of receptor activity as follows:

$$P_1=\ln \left(\frac{R_{\mathrm{v}}}{R_{\mathrm{h}}}\right).$$ [10]

The activity of two P₁, each viewing different objects a and b are then compared using following formula:

$${\mathrm{PD}}_{\mathrm{a},\mathrm{b}}=\frac{\left|P_{1,\mathrm{a}}-P_{1,\mathrm{b}}\right|}{2\left(\ln 10\right)},$$ [11]

which indicates polarization contrast between these objects. Furthermore, we applied normalized activity level of P₁ interneuron (P’₁) for each pixel based on equation as follows:

$$P_1\prime =\frac{P_1}{2\left(\ln 10\right)}.$$ [12]

With this P’₁, PD between two pixels, a and b can be described as

$${\mathrm{PD}}_{\mathrm{a},\mathrm{b}}=|P{\prime }_{1,\mathrm{a}}-P{\prime }_{1,\mathrm{b}}|.$$ [13]

From the photopolarimetry of a female and a male in noncourtship situation (NC) and a male during the courtship display (CD), we calculated P’₁ for each pixel, and produced a false-color map representing P’₁, where strong stimuli to R_h result in a negative P’₁, represented as yellow, whereas strong stimuli to R_v result in a positive P’₁, represented as blue. The entire arm region in the polarimetry image was then selected and P’₁ histogram was generated. For the courtship display photopolarimetry, P’₁ values were calculated for specific regions at the tips of the SDAs (Back tip and Front tip). To evaluate polarization contrast against the background, it is necessary to simulate the polarization state of the background. Under the sea, the background AoLP is considered to be predominantly “horizontal” while DoLP varies depending on turbidity and depth (24, 44). Reference was made to a previous study (24) which measured in situ DoLP under water in several areas differing in turbidity. The Secchi depth of the seawater at the sites of capture of D. andreanum was a mean of 13 m (25), so the DoLP measurement reference of the area in which Secchi disc visibility was from 10 to 13 m was chosen, since it mostly represents the natural habitat of D. andreanum. Since the measured DoLP in the reference was in the range of 0.1 to 0.2, at depths of 10 to 20 m, this range was used as the possible background DoLP in this study. PD was calculated for the whole arm region of female and male (NC/CD) against this approximated background of horizontal AoLP and estimated DoLP. Also, to evaluate polarization contrast within the arm pattern, a SD of P’₁ was calculated and compared among them.

Microscopic Observation of Iridophores.

Fixation.

Both male and female specimens were initially anesthetized with approximately 2% MgCl₂ in sea water and euthanized by an overdose of MgCl₂ prior to fixation according to the approved procedure by the Life Science Research Ethics and Safety Committee of the University of Tokyo (P20-7 and P21-16) (45). The arms II of both sexes were ablated and pinned to a plastic board. The arms were prefixed with 4% glutaraldehyde in 0.1 mol. L⁻¹ cacodylate buffer (pH 7.4). The arms were cut into four blocks of equal lengths, and the most distal block (i.e., closest to the tip) of each arm was then transferred to individual tubes containing the same fixative, and stored at 4 °C overnight. Samples were additionally fixed in 1% osmium tetroxide for an hour. The fixed samples were then washed and dehydrated through an ethanol series, followed by propylene oxide, and embedded in Epon 812.

Light microscopy.

For light microscopic (LM) observations, the blocks were cut into transverse sections of about 2 μm thickness, ensuring that each section included the entire region of the arm, using a diamond knife (Sym Knife Histo, Syntek, Japan) on a microtome (EM UC7, Leica, Germany). These sections were then stained with Toluidine Blue. Micrographs of these sections were obtained with an LM (Axioimager M1, Zeiss, Germany, BX51, Olympus, Japan) connected to a digital camera (AxioCam 506 color, Zeiss, Germany, DP71, Olympus).

Transmission electron microscopy.

Ultrathin sections (about 80 nm) were cut from several areas of the same block as those for light microscopy with a diamond knife (ultra45°, Diatome, Switzerland) and mounted on carbon/formvar-coated single-hole copper grids. The sections were stained with uranyl acetate and lead citrate and observed using an electron microscope (JEM-1400, JEOL Ltd., Japan) at 80 kV. Images were acquired at 11.46 nm/pixel (at a magnification of ×1,500).

Optical Analysis of Transmitted Light.

Specimens.

The left SDA of male D. andreanum, following euthanasia with 2% MgCl₂ (45) according to the approved procedure by the Life Science Research Ethics and Safety Committee of the University of Tokyo (P20-7 and P21-16) or natural death, was collected from several specimens. The epidermis was removed from each area to reveal the underlying muscle layer. At this stage, these areas were notably transparent (Fig. 4A).

Optical Experiment 1: Measurements of the polarization state of transmitted light.

The experimental setup described in Fig. 4A was constructed in a dimly lit room to avoid the effects of ambient light. A transparent glass container was filled with seawater and placed on a stand, and two small rubber stages were set inside. This glass container was confirmed to produce no birefringence, thereby not influencing the polarization state of the light. A camera (PL-B956U, Pixelink) fixed on a tripod and set above the glass container was connected to a PC and operated by the application (Pixelink Capture, Pixelink). The angle coordinates in this experiment were determined such that, as viewed from the camera’s perspective, the right side was set to 0° and counterclockwise was defined as positive. The sample arm was pinned to a piece of rubber and placed in the tank such that the tip of the arm was directed along the 180º direction and the middle region of the arm was positioned at the center of the camera’s field of view. The ventrolateral side of the SDA facing toward the female during the courtship display was oriented upward (Figs. 3J and 4A). With these settings, the angle 0º in this experiment corresponds approximately to the horizontal direction from the female perspective during the courtship display. Below the glass container, a monowavelength LED light source (λ = 525 nm) with a diffuser illuminated the glass container. Between the glass container and light source, a polarizer (P-A) was situated with its transmission axis angle at 0°, illuminating the glass container from behind with light polarized at 0º. This setting imitates the expected route of the light where horizontally polarized light reflected from the iridophores is transmitted through the SDA. To determine the AoLP of the transmitted light, the analyzer (an additional polarizer, P-B) was placed between the container and the camera. This polarizer, affixed to a rotating stage equipped with an angle scale, allowed for rotation in the horizontal plane and precise angle measurements. This setup enabled the capture of the polarized light passing through the arm and then through P-B. P-B was rotated by 5° increments, and images were captured at each angle through to 175°. The camera shutter speed was calibrated to ensure that the pixel values of the sample in the images remained below 70% of the maximum pixel value, to prevent overexposure. From the image taken, two regions of interest were selected: the arm (ROI_out) and the background (ROI_in), measuring 20 × 5 pixels (Fig. 4B). Suffixes in and out represent incident and output light waves, respectively. In ROI_in, the illuminating light is not transmitted through the arm. Thus, the AoLP of the ROI_in (AoLP_in) can be treated as that of the illuminating light. The green channel was taken as intensity I since it represents most closely the wavelength of background light. The angle dependence on the intensity can be expressed by Eq. 1 including three parameters (α, β, γ) as shown in SI Appendix, Fig. S10. The three parameters were estimated using the least squares method for the nonlinear regression model. When a coefficient of determination r² for each fitting was less than 0.90, those results were excluded from further analysis. From these parameters, AoLP and DoLP of each ROI can be calculated from Eqs. 2 and 3. Since AoLP has a periodicity of 180º, the estimated AoLP was adjusted by adding or subtracting 180° to ensure values fall within the range of 0 to 180°.

Optical Experiment 2: ΔAoLP and DoLP change associated with AoLP_in.

To investigate the optical mechanism contributing to AoLP and DoLP changes during transmission through the SDA, the AoLP and DoLP of transmitted light were measured using a modified experimental set up, and the results were analyzed using an optical model that included both linear and circular birefringence. In the previous experiment, the AoLP of illuminating light was fixed at 0º. This time, by rotating P-A, the AoLP of the illuminating light was changed from 0° to 175° in 5° increments, and instead of the previous CMOS camera, the polarization camera previously used in the behavioral experiment was mounted in the same position, and the photopolarimetry of the SDA sample was measured from above. From these photopolarimetry measurements, two regions of interest were selected: the arm (ROI_out) and the background (ROI_in), each measuring 50 × 10 pixels. AoLP and DoLP were calculated for each ROI.

As the aim was to determine the extent to which AoLP changed due to transmission through the SDA, ΔAoLP was calculated by subtracting AoLP_in from AoLP_out.

An optical model was developed to explain the ΔAoLP and DoLP patterns with the change of AoLP_in. The optical model considers the effect of circular birefringence, linear birefringence, and depolarization. The depolarization is included to account for the effects of light scattering. The initial AoLP and DoLP before light transmission through the arm are the same as those of AoLP_in and DoLP_in, respectively. First, we consider the effects of linear birefringence with phase retardation $\varphi$ between two orthogonal light waves. Based on equations in a previous study (46), when one of two principal axes is along the direction expressed by the angle $\chi$, ΔAoLP can be calculated as

$$\mathrm{\Delta }{\mathrm{AoLP}}_{\mathrm{LB}}=\frac{1}{2}\arctan \left(\tan \left(2·\left({\mathrm{AoLP}}_{\mathrm{in}}-\chi \right)\right)·\cos \varphi \right)+\chi -{\mathrm{AoLP}}_{\mathrm{in}}.$$ [14]

This equation gives values ranging from -180 to 180º. 180º is added when the value is negative so that $\mathrm{\Delta }{\mathrm{A}\mathrm{o}\mathrm{L}\mathrm{P}}_{\mathrm{L}\mathrm{B}}$ ranges from 0 to 180º, since it expresses the difference in polarization direction. It should be noted that the direction of AoLP change is not explicitly determined in this experiment. For example, if ΔAoLP is 92°, it is unclear whether the rotation was 92° in the positive (counterclockwise) direction or 88° in the negative (clockwise) direction. One of the simplest applications of Eq. 14 is the case of the half wave plate, where $\varphi$ = 180°, $\chi$ = 0°, and ${\mathrm{AoLP}}_{\mathrm{in}}$ = 45°. By substituting these values, $\mathrm{\Delta }{\mathit{AoLP}}_{\mathit{LB}}$ is calculated to be +90º, consistently with the function of the half wave plate. When the incident light polarization is along the principal axis of the phase retarder, i. e., ${\mathrm{A}\mathrm{o}\mathrm{L}\mathrm{P}}_{\mathrm{i}\mathrm{n}}=\chi$, there is no effect on the polarization direction, and thus $\mathrm{\Delta }{\mathrm{A}\mathrm{o}\mathrm{L}\mathrm{P}}_{\mathrm{L}\mathrm{B}}=0$. Thus, it is necessary to include another effect to explain the experimentally observed constant shift in $\mathrm{\Delta }{\mathrm{A}\mathrm{o}\mathrm{L}\mathrm{P}}_{\mathrm{L}\mathrm{B}}$ as shown in Fig. 4F. Circular birefringence was introduced in the optical model, which constantly increases ΔAoLP independently of the AoLP of the incident light. When polarization rotation by circular birefringence is represented by ψ, the overall AoLP change (ΔAoLP) is

$$\mathrm{\Delta }\mathrm{AoLP}=\mathrm{\Delta }{\mathrm{AoLP}}_{\mathrm{LB}}+\psi .$$ [15]

For DoLP, the linear birefringence effect is expressed as

$${\mathrm{DoLP}}_{\mathrm{LB}}={\mathrm{DoLP}}_{\mathrm{in}}\sqrt{1-{\sin }^2\left(2·\left({\mathrm{AoLP}}_{\mathrm{in}}-\chi \right)\right)·{\sin }^2\phi }.$$ [16]

Circular birefringence does not influence DoLP. Therefore, considering the depolarization effect (μ) due to scattering, DoLP_out is represented as

$${\mathrm{DoLP}}_{\mathrm{out}}=\mu ·{\mathrm{DoLP}}_{\mathrm{LB}}.$$ [17]

AoLP and DoLP data were analyzed from eight specimens using these models. DoLP_in was approximated to 1. Parameters χ, φ, ψ, and μ were determined by nonlinear least squares fitting. Initially, χ, φ, and ψ were optimized with AoLP_out data. Subsequently, μ was estimated with DoLP_out data using fixed χ and φ. Model performance was assessed by calculating the coefficient of determination (r²).

Optical Experiment 3: Evaluation of optical path dependence of ΔAoLP.

The relationship between |ΔAoLP| and arm areas was also explored. At the three areas (0.25, 0.5, and 0.75) along the arm, with 0 defined as the base and 1 as the tip (Fig. 5A), |ΔAoLP| was measured by repeating Optical Experiment 1. AoLP_out was again derived based on Eqs. 2 and 3. The rotation direction of AoLP was determined by the ΔAoLP of each color channel in the additional optical experiment with use of white LED (See SI Appendix, Text for detail). Analysis was performed only on those specimens whose coefficient of determination (r²) exceeded 0.90 in measurements at all three areas (n = 6).

Morphological Measurement.

From the dead specimens of mature D. andreanum collected from commercial fishing vessels using bottom trawls, male SDA and corresponding female arm (arm II) were dissected and photographed with a digital camera (TG-6, Olympus, Japan). From those images, the arm width was measured at five positions (0, 0.25, 0.5, 0.75, and 0.95) along the arm, with 0 defined as the base and 1 as the tip (Fig. 5A).

Supplementary Material

Appendix 01 (PDF)

Movie S1.

Photo-polarimetry video of courtship display. Left: normal RGB image. Right: false-color image representing AoLP and DoLP.

Data, Materials, and Software Availability

The original data are available on Dryad (https://doi.org/10.5061/dryad.41ns1rnsh) (47).