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First published online August 9, 2007
Journal of Experimental Biology 210, 2801-2810 (2007)
Published by The Company of Biologists 2007
doi: 10.1242/jeb.006965

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The imaging properties and sensitivity of the facial pits of pitvipers as determined by optical and heat-transfer analysis

George S. Bakken^1,* and Aaron R. Krochmal²

¹ Department of Ecology and Organismal Biology, Indiana State University, Terre Haute, IN 47809, USA
² Department of Natural Sciences, University of Houston – Downtown, 1 Main Street, Houston, TX 77002, USA

^* Author for correspondence (e-mail: gbakken{at}indstate.edu)

Accepted 11 June 2007

	Summary

TOP Summary Introduction Materials and methods Results Discussion References

 
It is commonly assumed that the facial pit of pitvipers forms relatively sharp images and can detect small differences in environmental surface temperatures. We have visualized the temperature contrast images formed on the facial pit membrane using a detailed optical and heat transfer analysis, which includes heat transfer through the air in the pit chambers as well as via thermal infrared radiation. We find the image on the membrane to be poorly focused and of very low temperature contrast. Heat flow through the air in the pit chambers severely limits sensitivity, particularly for small animals with small facial pit chambers. The aperture of the facial pit appears to be larger than is optimal for detecting small targets such as prey at 0.5 m. Angular resolution (i.e. sharpness) and image strength and contrast vary complexly with the size of the pit opening. As a result, the patterns of natural background temperatures obscure prey items and other environmental features, creating false patterns. Consequently, snakes cannot simply target the strongest signal to strike prey. To account for observed behavioral capabilities, the sensory endings on the pit membrane apparently must respond to temperature contrasts of 0.001°C or less. While neural image sharpening likely enhances imaging performance, it appears important for foraging snakes to select ambush sites offering uniform backgrounds and strong thermal contrasts. As the ancestral facial pit was likely less sensitive than the current organ, objects with strong thermal signals, such as habitat features, were needed to drive the evolution of this remarkable sense.

Key words: pit viper, facial pit, optics, heat transfer, image analysis, sensory physiology, snake

	Introduction

TOP Summary Introduction Materials and methods Results Discussion References

 
It has been known for some time that the eponymous facial pits of pitvipers (Viperidae: Crotalinae) are sense organs that respond to thermal infrared radiation emitted by nearby surfaces (ca. 5–30 µm wavelength), and can thereby sense the temperature of surrounding surfaces (Bullock and Cowles, 1952). Functionally, the facial pits are image-forming structures based on pinhole optics resembling the chamber-type eye of the nautilus (Fernald, 2006). We have a general sense of some behavioral functions, and various aspects of the anatomy and neurophysiology of the facial pit are well documented. But, we lack clear understanding of the physical and physiological optics of the facial pit system, and thus of what pitvipers can actually `see' with the facial pits.

Behavioral studies have established that the facial pits aid in prey acquisition (Bullock and Diecke, 1956; de Cock Buning, 1983; Kardong, 1986; Noble and Schmidt, 1937) and mediate behavioral thermoregulation (Krochmal and Bakken, 2003). Other functions have been proposed but not tested, including general navigation and predator detection (Bullock and Barrett, 1968; Greene, 1992; Sexton et al., 1992). Behavioral evidence suggests that input from the facial pits compensates for visual deprivation (Kardong and Berkhoudt, 1999; Kardong and Mackessy, 1991). Thus, this sense may be particularly important on moonless nights, when both rattlesnakes and their rodent prey appear to be most active (Clarke et al., 1996), as well as when surface temperature itself is relevant, as in behavioral thermoregulation (Krochmal and Bakken, 2003; Krochmal et al., 2004).

Anatomically, the facial pits are located between the eyes and nostrils (Fig. 1A). Each consists of a 1–3 mm diameter aperture expanding internally to form an asymmetric and somewhat irregular mushroom-shaped cavity (Fig. 1B). Thermal radiation entering the aperture falls on and heats a sensory membrane suspended in the back of the pit, dividing the pit cavity into an inner and outer chamber. The membrane contains a few thousand receptors that respond to membrane temperature changes of 0.003°C or less (Bullock and Cowles, 1952; Bullock and Diecke, 1956; de Cock Buning, 1983; Moiseenkova et al., 2003).

View larger version (81K): [in this window] [in a new window]   Fig. 1. (A) Close-up view of the head of a western diamondback rattlesnake Crotalus atrox Baird and Girard 1853 showing the location of the pit organ. (B) Frontal section showing the internal structure of the pit organ of a Pacific rattlesnake Crotalus o. oreganus Holbrook 1840. To aid visualization, the anterior air chamber was filled with red acrylic before the entire head was infiltrated and embedded. However, this may have displaced the membrane closer to the back of the posterior chamber. The angular aperture i varies from 23° (included angle 45°) laterally to 10° (included angle 20°) when looking ahead and to the contralateral side.

The design and interpretation of studies of both behavioral responses and neural processing requires knowledge of the temperature contrast image on the membrane, which is defined by the optical and the heat transfer properties of the facial pit. Angular resolution (the sharpness of the image) determines the `brightness' of small targets, the extent to which larger objects such as food items contrast with background clutter, and the overall quality of spatial information available for tasks such as general navigation and thermoregulation. Background and target surface temperatures as well as surface temperature contrasts are affected by air temperature, current and past solar radiation, and the heat storage capacity of the object. Thus, thermal contrast varies with habitat structure and time of day, creating spatiotemporal variation in the probability of success of behavioral activities hinging on thermal cues.

Limited understanding of the relevant optical and thermal physics of the facial pits is a common deficiency of existing studies. For example, a theoretical analysis of pit sensitivity (Jones et al., 2001) severely overestimated absorption of thermal radiation by the atmosphere and concluded that absorption limited the pit organ to a range of a few cm (Bakken, 2007). A number of researchers have presented pitvipers with thermal stimuli having surface temperatures equal to or exceeding body core temperature of typical prey items (e.g. Bullock and Barrett, 1968; Goris et al., 2000; Goris and Nomoto, 1967; Hartline et al., 1978; Pappas et al., 2004). However, the furred and feathered surfaces covering most of the body are actually closer to air temperature (e.g. Hill et al., 1980; Hill and Veghte, 1976; Kardong, 1986; Veghte and Herreid, 1965). Behavioral experiments have typically used a single target against a uniform thermal background. This may overestimate performance in natural habitats, because the angular resolution of the pit organ is likely poor (Otto, 1972; Stanford and Hartline, 1984). As a result, the radiation from small, warm objects is spread over a large area of the pit membrane and blended with non-uniform natural thermal backgrounds. The only experimental study known to have examined background effects (Theodoratus et al., 1997) placed test targets behind aquarium glass, which is completely opaque to thermal radiation (Hsieh and Su, 1979). Consequently, the reported responses are experimental artifacts.

The foregoing review shows that there is a need for a comprehensive study that will define the input to the sensory system of a pitviper under relevant natural situations. Such a study requires detailed knowledge of the physical optics of the facial pit and its heat transfer properties. Prior studies (de Cock Buning, 1984; Otto, 1972) examined the distribution of radiation from a point source over the pit membrane using simplified geometric models, but lacked the modern computational tools needed to translate this information into a representation of the temperature contrast image on the pit membrane. Further, these studies omitted potentially important heat transfer processes such as convection and conduction from the pit membrane.

To fill this need, we have analyzed the facial pit as an optical system and used heat transfer analysis to convert image irradiance to membrane temperatures on the basis of published physiological data. We then obtained radiometric thermograms of some realistic natural habitats to determine the typical surface temperatures and temperature contrasts present. Finally, we used the results of our optical and heat transfer analysis and image processing software to manipulate these thermograms to generate corresponding representations of the image falling on the facial pit membrane. The processed images indicate the general characteristics of the sensory input to the facial pit sensory system in various ecologically meaningful situations, and provide insights that can aid the design and interpretation of behavioral and neurophysiological studies.

Theory: optics of the pit organ
Overview
The facial pit is essentially a pinhole camera consisting of a lensless aperture in front of a detector (the pit membrane) that forms the image plane (Fig. 1B). Radiation simply passes through an opening (the optical pupil) without deflection and falls on the image plane. Facial pit apertures are large enough relative to pit depth that diffraction may be neglected, and thus elementary geometric optics and photometric analysis can be used (Born and Wolf, 1970). Briefly, the light from a point on the source object that passes through the aperture irradiates a defined area on the image plane, called the point spread function. The image is formed by overlapping spread functions, and, as demonstrated later, is either sharp but dim when the optical pupil is small, or bright but blurred when it is large. We will follow de Cock Buning (de Cock Buning, 1984) and model the facial pit as a circular aperture of radius r_a located a distance d from the image plane (Fig. 2). Though a simplification of the geometry in Fig. 1B, this model is adequate to illustrate the main features of the optics of the facial pit. The analysis proceeds in three steps and follows standard procedures (Born and Wolf, 1970).

View larger version (9K): [in this window] [in a new window]   Fig. 2. Spherical coordinate system used in Eqn 2 and Eqn 4 to compute radiance and irradiance. The symbol d=sindd denotes an element of solid angle.

Both source and image are characterized by their radiance B (W m^–2 sr), defined as the radiant flux, d (W) per unit solid angle (steradians) emitted by or falling on an element of surface area dA (m²). Source and image radiance can be related to the surface temperature of the source object, T_o (kelvins, K=273.15+°C; absolute temperatures in kelvins must be used in thermal radiation calculations; temperature differences or changes may be either K or °C). The total radiant flux (W) emitted from dA is given by the Stefan–Boltzmann law,

(1)

where =5.67x10^–8 W m^–2 K^–4, and the emittance of the surface is (01). Total radiant flux may also be computed by integrating source radiance B_o over a hemispherical solid angle,

(2)

where and are spherical coordinates. Combining Eqn 1 and Eqn 2 gives the relation between radiance and object temperature:

(3)

There are no optical elements, and thus no reflection or absorption losses in pinhole optics. Thus, conservation of energy requires that the radiance of the image B_i equals the radiance of the source object B_o (Born and Wolf, 1970).

Conversion of image radiance to membrane temperature
We must now convert the irradiance contrast into the temperature contrast that is detected by the pit membrane receptors. The pit membrane absorbs ca. 50% of incident thermal radiation (wavelength 5–30 µm), and so half of the image irradiance is absorbed and converted to heat, forming a temperature contrast image (Bullock and Diecke, 1956; Goris and Nomoto, 1967). This is detected by sensory receptors that respond to membrane temperature changes of 0.003°C or less (Bullock and Diecke, 1956; de Cock Buning, 1983; de Cock Buning et al., 1981). There is no evidence for quantum detection (Moiseenkova et al., 2003).

The temperature at a point on the membrane is determined by the local balance between radiant heat transferred from the source object and other sources of heat gain and loss. The heat storage capacity of the membrane is important only for transient stimuli. Lateral conduction within the membrane may reduce angular resolution somewhat (DeSalvo and Hartline, 1978), but has a negligible effect on the heat balance.

The total irradiance (W m^–2) at an image point (x,y) on the pit membrane is the sum of the image irradiance from the source object E_i(x,y), plus the background irradiance from the various walls of the pit, Q_pit. The image irradiance is found by integrating the image radiance B_i=B_o over the solid angle of the exit pupil, i.e. over the pinhole aperture as seen from (x,y). For our facial pit model, a simple circular aperture of radius r_a a distance d from the image plane (Fig. 2), the exit pupil is a circle with its center normal to point (x,y), subtending a half-angle of _i=arctan (r_a/d). Integrating over the solid angle subtended by this exit pupil and applying Eqn 3, the image irradiance is:

(4)

Heat is exchanged between the facial pit membrane and the surrounding air primarily by conduction. The membrane is shielded from forced convection by its location in a semi-enclosed pit (Bullock and Diecke, 1956), and wind speed near the ground is very low (Gates, 1980). For free convection to occur within an enclosure, the Grashof number Gr must exceed 1000 (Eckert and Carlson, 1961). As Gr

Conductive heat transfer through the air inside the pit chambers from a point on the membrane at a temperature T to the opposite pit wall at a temperature T_p is approximately

(5)

Here, Q_air is the amount of heat lost by conduction through the air to the pit walls (W m^–2), k is the thermal conductivity of air (0.026 W m^–1 °C or W m^–1 K), z is the effective distance from the membrane to the wall of the outer (anterior) chamber, and w is the effective distance to the wall of the inner (posterior) chamber.

At any point on the pit membrane (x,y), the energy lost by radiation and convection from both sides of the membrane must equal the radiant energy gained from the pit walls, Q_pit, and from the source object, E_i. If the temperature of an image point denoted by subscript 1 is and the temperature of the corresponding source object point is T₁, then:

(6a)

Substituting for E₁ using Eqn 4,

(6b)

If the temperature of an image point denoted by subscript 2 is and the temperature of the corresponding object point is T₂, then:

(7)

The factor of 2 on the left side of Eqn 6 and Eqn 7accounts for the emission of thermal radiation from both the front and back surfaces of the pit membrane.

The facial pit membrane responds to the contrast between a target and its background, (), rather than absolute temperature (Bullock and Barrett, 1968; Grace and Van Dyke, 2005). The temperature contrast of the ideal image is given by combining Eqn 6 and Eqn 7,

(8)

By Kirchoff's law (conservation of energy), the membrane emittance for thermal radiation _m equals its absorptance, _m, and thus for simplicity we use only _m. As natural surfaces have 0.95–0.97, Eqn 8 has been further simplified by the approximation =1.

Under natural conditions, the differences among snake, object, and background temperatures are small (ca. 10 K) compared to their absolute temperatures (ca. 300 K). This allows Eqn 8 to be linearized about a convenient reference temperature (Bakken, 1976), so that . Defining , the temperature contrast between points 1 and 2 is:

(9)

Computing actual image using point spread function
A pinhole camera produces a geometrically perfect image, but the radiation from a single source point is spread over an area of the image called the point spread function. The radiance at a given point (x,y) on the membrane is the sum of the radiation from all the point spread functions that overlap (x,y). Consequently, the image on the membrane is `fuzzy' and has less contrast than the corresponding ideal image.

Mathematically, the real temperature distribution over the image plane T'(x,y), is found by convoluting the temperature distribution of the ideal image, , with the point spread function S(x–, y–). Here, (x,y) is the coordinate of the point of interest and (,) is the coordinate of an ideal image point contributing energy to (x,y). Strictly, the convolution should precede the heat transfer calculation, but this procedure is computationally more convenient and the final result is the same because the relation between irradiance and temperature (Eqn 9) is effectively linear.

For our model of the facial pit (Fig. 2), the point spread function is approximately

(10)

The real temperature contrast image is computed using

(11)

Conservation of energy requires that the result be normalized by the integral of the spread function (denominator).

	Materials and methods

TOP Summary Introduction Materials and methods Results Discussion References

 
To investigate the consequences of variation in the spatial resolution and receptor sensitivity of real and hypothetical facial pits, we derived representations of the blurred image on the pit membrane using the above analysis. As approximations to the ideal image, we used sharply focused thermograms of various scenes recorded with a resolution of 0.1°C and an absolute accuracy of 1–2°C using a FLIR PM575 radiometric thermal imager (FLIR Inc, North Billerica, MA, USA). We computed the membrane temperature contrasts using Eqn 9, and then convoluted these images using Eqn 11 as implemented in MATLAB (The MathWorks, Inc. Natick, MA, USA). We used the `circular' option in MATLAB to reduce edge artifacts. The output is our representation of the approximate appearance of the temperature contrast images on the pit membrane.

We explored the interrelated effects of angular aperture on image sharpness and membrane temperature contrast by using spread functions with _i from 2.5° to 20°. The observed angular apertures for Crotalus oreganus (Fig. 1B) are ca _i=20–30° to the side, and ca. 10° in the forward direction (see also DeSalvo and Hartline, 1978). The importance of forward imaging is indicated by a higher density of receptors and associated blood vessels on the portion of the membrane corresponding to objects directly in front of the head (Amemiya et al., 1999; Goris and Nomoto, 1967; Goris and Terishima, 1973). Viewed from the forward direction, the external aperture is higher than it is wide (Fig. 1A) and the optical spread function is therefore sub-elliptical. To simulate this, we used elliptical spread functions with the horizontal _i half of the vertical _i.

View larger version (45K): [in this window] [in a new window]   Fig. 3. (A) Thermogram of an Ord's kangaroo rat Dipodomys ordii taken in a laboratory enclosure set at 15°C, scaled to represent an 80° field of view with the animal 25 cm distant. (B–D) The results of convoluting that image with circular spread functions with the indicated half-angles i). (E) The same animal imaged at 30°C. Both A and E use the same color representation of temperature and are marked with the full range of temperatures visible in each. (F–H) The results of convoluting that image. The color steps in B–D and F–H indicate temperature contrasts of 0.001°C. While spatial resolution is good at 15°C for the hypothetical i=5°(D), contrast is only 0.003°C and the kangaroo rat is essentially invisible at 30°C (H). Temperature contrast is somewhat greater for i=10° and 20°, 0.006°C in the 15°C cabinet, and 0.002–0.003°C in the 30°C cabinet.

	Results

TOP Summary Introduction Materials and methods Results Discussion References

 
Signal strength and ambient temperature
Environmental conditions have a strong effect on source temperature contrasts, particularly for mammalian and avian prey. The surface temperature of fur or feather insulation is closer to air than body core temperature (e.g. Hill et al., 1980; Hill and Veghte, 1976; Kardong, 1986; Veghte and Herreid, 1965). To illustrate, we recorded thermograms (Fig. 3A,E) of a potential prey item in a temperature cabinet at the lowest body temperature of active rattlesnakes, 15°C, and at the typical hunting temperature of 30°C (Beck, 1995; Hirth and King, 1969; Moore, 1978). While the temperature contrast over most of the 60 g Ord's kangaroo rat Dipodomys ordii is greatest at 15°C, over most of the fur surface it is only about 6°C above air temperature. This is less than 1/3 of the 21°C difference between body core (36°C) and air temperature. At 30°C, temperature contrast is about 2.5°C, compared to the 6°C difference between core and air. Only the eyes have a surface temperature near body core temperature. The results for other bird and mammal prey items we examined are similar, although some thinly furred ground squirrels had higher fur temperatures.

Angular aperture, resolution, and signal strength
The size of the angular aperture of the pit influences both resolution and signal strength. Fig. 3B–D,F–H are representations of the temperature contrast images on the membrane of a 3 mm total diameter pit with the membrane located 0.75 mm from the back wall and various _i from 20° to 5°. Colorbar steps correspond to membrane temperature differences of 0.001°C, near the lower end of the sensitivity range suggested by Bullock and Diecke (Bullock and Diecke, 1956). Resolution is lower but temperature contrast is greater for larger pit apertures.

Non-uniform background effects
The laboratory images have a uniform contrasting background, while natural thermal backgrounds are strongly patterned. To investigate the potential impact of background pattern on prey targeting, we recorded outdoor thermal images of a variety of targets. Fig. 4A is an image of two mice recorded in open scrub habitat at midnight following a mostly cloudy day. Based on Fig. 3, thermal imaging conditions were nearly optimal for the snake (air temperature, 15°C; surface temperature 11–13°C). Nevertheless, the contrast of the convoluted images (Fig. 4B–H) is low and the mice hard to detect with color steps of 0.001°C. For clarity, we exaggerated contrast by using color steps of 0.0005°C.

View larger version (53K): [in this window] [in a new window]   Fig. 4. (A) Thermogram of two mice, scaled for an 80° field of view with the animals 45 cm distant. Images were recorded at an air temperature of 15°C in sparse scrub habitat around midnight, following a mostly cloudy afternoon. (B–D) Image A convoluted with circular spread functions chosen to visualize the image along the optic axis of the facial pit. (E–G) Image A convoluted with elliptical spread functions to visualize imaging directly in front of the snake (right column). The i indicated for each row is the aperture angle of a circular spread function (B–D), and the vertical i of an elliptical spread function (E–G). The minor axis i of the ellipse is half that of the vertical axis. The temperature contrast in these images is quite low, so for clarity we have assumed a larger pit and greater membrane sensitivity (color steps of 0.0005°C) than in Fig. 3. Note that, particularly for large i (poor resolution), the warmest part of the image is a large, warm area of ground and not the mice.

View larger version (16K): [in this window] [in a new window]   Fig. 5. Effect of conduction through still air in the pit on the ratio of image to source temperature contrast for facial pits with i=20° and various dimensions and membrane positions. The x-axis is the thickness of the posterior chamber and indicates the position of the membrane from touching the back of the posterior chamber (thickness 0) to the center of the chamber (thickness equal to half the total thickness of the pit), as indicated by the inset drawings based on Fig. 1B. The y-axis is the temperature contrast on the pit membrane for a 1°C source temperature contrast. If conduction through the air surrounding the membrane is neglected as in prior studies, this ratio is 0.058 for pits of all sizes and configurations.

The consequences of varying facial pit dimensions are visualized in Fig. 6. We computed temperature contrast images for facial pits from 1 to 4 mm total thickness with the pit membrane 25% of the total thickness from the wall of the posterior chamber and both circular (Fig. 6B–D) and elliptical (Fig. 6E–G) spread functions with _i=20°. Even assuming a high membrane sensitivity (color steps 0.0005°C), the mice are indistinct to invisible when the total thickness of the facial pit is 2 mm thick or less.

View larger version (57K): [in this window] [in a new window]   Fig. 6. The effect of facial pit size on membrane temperature contrast. The original thermogram (A) used in Fig. 4 has been processed to show membrane temperature contrasts for facial pits both on the optic axis of the pit (B–D) and directly in front of the snake (E–G). The total thickness, including both the outer and inner chambers, is indicated for each row. The membrane is assumed to be 25% of the total diameter from the wall of the posterior chamber. The temperature contrast on the pit membrane is indicated by color steps of 0.0005°C.

View larger version (74K): [in this window] [in a new window]   Fig. 7. Two situations relevant to pitviper biology present particularly strong surface temperature contrasts. (A) A rodent burrow below a desert shrub at high noon, scaled to an 80° view angle with the burrow 28 cm distant. Conditions are warm but not extreme, with air temperature of 33°C and peak ground temperatures near 50°C. (B–D) Pit membrane temperature contrasts visualized using the indicated i. The burrow could be easily identified from a distance by a snake leaving the shade of a bush to seek underground shelter. (E) An American cardinal Cardinalis cardinalis viewed against a clear sky, scaled to an 80° view angle with the cardinal 31 cm distant. Note that the thermal imager does not record radiant sky temperature properly, and so the sky has been rescaled to a radiant temperature of 5°C on the basis of Swinbank's formula (Swinbank, 1963). (F–H) Pit membrane temperature contrasts visualized using the i indicated for that row. The temperature contrast on the pit membrane in B–D and F–H are indicated by color steps of 0.001°C.

Another situation providing strong contrast against background is a warm-blooded prey item viewed against a clear sky, which emits little thermal radiation (Swinbank, 1963). This is illustrated in Fig. 7E–H, which shows a cardinal (Cardinalis cardinalis) viewed against the sky at an air temperature of 20°C. The 5°C radiant temperature of the sky contrasts strongly with the 30°C feather surface temperature of the bird, and creates an 0.01°C membrane temperature contrast even with the smallest angular aperture (_i=5°).

	Discussion

TOP Summary Introduction Materials and methods Results Discussion References

 
Signal loss by conduction through air and estimates of receptor sensitivity
Our findings indicate either that the membrane is more sensitive than currently estimated, or that pitvipers obtain less information from this sense than is commonly believed. Accounting for conductive heat loss through still air in the anterior and posterior chambers reduces the temperature contrast of the image to only 5–25% of that estimated by earlier studies, which did not consider conduction through the air (Fig. 5). To achieve the observed behavioral capabilities of pitvipers (Ebert and Westhoff, 2006), the contrast sensitivity of the pit membrane needs to be at the most sensitive end of the range (0.003–0.001°C) found by Bullock and Diecke (Bullock and Diecke, 1956). Our analysis assumed the snake was on the ground, and thus did not include forced convection. Significant air movement with the exterior pit, e.g. because the snake was exposed to wind on an arboreal perch, would further reduce membrane temperature contrasts. Thus, the membrane may conceivably respond to contrasts of less than 0.001°C. The mechanism by which such sensitivity might be obtained is presently unknown.

Movement and time response
To simplify this preliminary study, we chose not to examine the effects of either heat storage in the pit membrane or target movement. Heat storage in the pit membrane would potentially slow the time response and cause blurring of moving targets. Experimental studies have reported maximum flicker fusion frequencies of 8 Hz or less, depending on flicker contrast (Bullock and Diecke, 1956). Goris et al. (Goris et al., 2000) has suggested that neurological control of pit membrane microcirculation may serve to increase time response, but this has not been demonstrated experimentally. Membrane receptor response is commonly regarded as phasic (Barrett et al., 1970; Bullock and Cowles, 1952) although some studies have reported tonic and phasic-tonic responses as well (Goris and Terishima, 1973). A primarily phasic response would presumably make the facial pit more sensitive to moving targets than stationary ones, although scanning head movements could make stationary targets equally conspicuous (Goris and Terishima, 1973). Behavioral and modeling studies are needed to confirm that these conclusions apply to overall sensory performance.

Growth and facial pit sensitivity
The effect of conductive heat loss through the air is inversely proportional to pit size. This suggests that the facial pit may be of limited value to juvenile snakes. Possibly as a result, juvenile pitvipers are known to depend more on ectothermic prey than do adults, although body size is also a factor. The observations that juvenile Gloydius shedaoensis preferentially select arboreal ambush sites where prey are viewed against the cool sky (Fig. 7E–H), and are slower and less accurate in their strikes (Shine et al., 2002b) might be explained by the reduced sensitivity of their smaller facial pit organs. However, direct evidence with which to test this hypothesis is lacking.

Is the angular aperture of the facial pit optimal?
Once the full angle of the facial pit (2_i) exceeds the angle subtended by the target, membrane irradiance is constant and the only effect of further enlarging the aperture is to impair resolution and increase background interference. In Fig. 3, the kangaroo rat at 0.5 m subtends a full angle of 10°, so that the optimal half angle _i is 5°, much smaller than the actual 10–22° _i of C. oreganus (Fig. 1B). As is evident in Figs 4 and 7, a small aperture may be advantageous even when target irradiance on the pit membrane is somewhat reduced because background interference is decreased more than the contrast between target and background. Thus, the facial pit aperture appears to be larger than optimal for detecting small objects, like prey, and it is not clear why the angular aperture of the facial pit is as large (_i=20–30°) as is observed. A large aperture provides more detectable contrast and might be used to reconstruct images with more angular resolution and contrast than could be produced with a smaller aperture. Similarly, the aperture might be optimized for detecting larger objects, including environmental features. This could facilitate behavioral thermoregulation, which has been proposed as the initial adaptive force that drove the evolution of the organ (Krochmal and Bakken, 2003).

Utilizing low angular resolution imaging
Several simple mechanisms have been proposed to explain how pits may function despite apparently low spatial resolution, including edge detection or the use of both pits as a null detector (e.g. Goris and Terishima, 1973). Our results call into question the utility of such simple mechanisms. Specifically, the spread function resulting from a large aperture blurs the edges of real targets, and the warmest part of the pit membrane may not represent the target when the background is not uniform (Fig. 4B,E).

A more credible alternative is that the imaging properties of the facial pit may be improved by image sharpening during post-processing in the central nervous system. If the blurred image has sufficiently fine discrimination of irradiance levels, and if the optical spread function is known, the inverse operation of Eqn 11 can reconstruct the original image in some detail. Image sharpening routines are included in many image processing programs such as MATLAB, and a hypothetical neural network procedure has been proposed specifically for pitvipers (Sichert et al., 2006), though empirical data to support it is lacking.

The quality of the processed image is closely linked to how accurately the spread function is known [chapter 5, Gonzalez and Wintz (Gonzalez and Wintz, 1977)]. The geometry of the facial pit, and thus the spread function, varies only with growth, if at all. Thus, the snake's neural network can potentially learn a single spread function, which can then be used to sharpen images. Indeed, it has been reported that the temperature contrast image on the facial pit membrane is sharpened by neural processing in the lateral descending trigeminal tract (LTTD) of the medulla (Berson and Hartline, 1988; Stanford and Hartline, 1980).

The spread function might be provided in two ways. First, neural interconnections between thermal and visual neurons have been reported in the optic tectum (Berson and Hartline, 1988; Hartline et al., 1978). It has been shown that some alternative spatial senses, such as acoustic prey location in owls, are fine-tuned to match visual input (Harris, 1986; Schnitzler et al., 2003), and the same may be true for the facial pit. Second, spread functions might be determined from facial pit input by using neural mechanisms analogous to forensic computer algorithms [chapter 5, Gonzalez and Wintz (Gonzalez and Wintz, 1977)] or the autofocus mechanism found in some cameras.

Foraging strategies and thermal backgrounds
Pitvipers commonly use an ambush foraging strategy (e.g. Reinert et al., 1984), and the coupled problems of thermal signal strength and angular resolution that we have documented suggest that predation effectiveness would be greater if pitvipers were to seek out ambush sites offering a contrasting and relatively uniform thermal background. Shine and Sun (Shine and Sun, 2002) conducted a 2-day study of thermal and visual background in pitvipers foraging on migrating birds and found that snakes indeed selected ambush sites that offered a cool sky background. Although snakes struck preferentially at warm targets, the importance of the facial pits was not entirely clear. The snakes generally left arboreal perches during the night and returned in the morning, and thus foraged primarily when ample visual illumination was available. Further, site selection was equally consistent with selecting areas of highest prey availability. Thermoregulation is another factor that might influence ambush site selection (Shine et al., 2002a). Clearly, this is a complex problem needing carefully designed field studies.

Facial pit evolution and scenes presenting strong thermal contrast
The ancestral facial pit likely had lower angular resolution and less temperature sensitivity than the modern organ. Thus, evolution of the facial pit is most likely to have occurred in a situation where large targets with strong temperature contrast were present, and the ability to sense them provided a selective advantage (Krochmal and Bakken, 2003; Krochmal et al., 2004). At least two situations provide high contrast (Fig. 7). First, the ability to sense thermal radiation may allow a snake to thermoregulate more effectively in a habitat characterized by strong temperature contrasts caused by solar radiation (Krochmal and Bakken, 2003). This scenario also provides large targets, minimizing the demands on angular resolution. Second, perching birds contrast strongly against the sky (Shine and Sun, 2002). Thus, although most extant pitvipers are heavy bodied and terrestrial in habit, the facial pits may have evolved initially to facilitate nocturnal predation on roosting birds or active bats in sparse deciduous vegetation, where they would be viewed against a clear night sky. The radiant temperature of a night sky is well below air temperature (Swinbank, 1963), so birds and mammals would contrast even if the insulating coat is at air temperature. A similar, but less extreme, contrast may exist between burrowing mammals and the burrow walls. Although most pitvipers are sedentary, many other snakes actively search burrows (Secor, 1995), and so the facial pit may have evolved initially to aid in burrow searching. To test these hypotheses, studies are needed to determine how extensively extant pitvipers use the facial pit sense in habitats imposing different thermal radiation backgrounds and different thermoregulatory demands. Careful attention to paleohabitat signatures associated with any discoveries of fossils of putative ancestral pitvipers might also indicate the relative merit of these scenarios.

Summation
Our survey of the approximate imaging properties of the facial pits leads us to conclude that the imaging properties of the pit organ are critical to understanding its function as a sensory organ and its role in the behavior and ecology of the animal. While there has been significant progress, many interesting studies of field and laboratory behavior and sensory neurophysiology remain to be done before we will fully understand this novel sensory organ and its role in the ecology of pitvipers.

List of symbols

radiant flux (W)

solid angle (sr; steradians)

emittance for thermal infrared radiation (01) (dimensionless)

spherical coordinate (rad)

i

half-angle of facial pit aperture as seen from (x,y) on pit membrane, _i=arctan (r_a/d) (rad)

spherical coordinate (rad)

(,)

coordinate of ideal image point contributing energy to (x,y)

(x,y)

coordinates of an image point of interest (m)

A

area (m²)

d

distance from aperture center to image plane (m)

d

element of solid angle (sr)

dA

element of surface area (m²)

E_i(x,y)

irradiance at image point (x,y) due to source object (W m^–2)

Gr

Grashof number (dimensionless)

Q_air

heat flow through the air to the pit wall by conduction (W m^–2)

Q_pit

background irradiance from pit walls falling on an image point (W m^–2)

R

equivalent conductance due to thermal radiation, R=4_mT_p³ (W m^–2 °C)

r_a

facial pit aperture radius (m)

S(x–, y–)

point spread function

T

membrane temperature at any particular point (°C or K)

temperature of the ideal image at point (,)

T₁`

temperature of the source object point corresponding to T₁ (°C or K)

T_o

surface temperature of the source object (K)

T_p

pit wall temperature (°C or K)

w

effective distance from membrane to the wall of the inner (posterior) chamber (m)

z

effective distance from membrane to the wall of the outer (anterior) chamber (m)

k

thermal conductivity of air, k=0.026

T₁

temperature at point 1 on pit membrane (°C or K)

B

radiance (W m^–2 sr)

B_i

radiance of the image (W m^–2 sr)

B_o

source (W m^–2 sr)

E

irradiance (W m^–2)

Stefan-Boltzmann constant, 5.67x10^–8 (W m^–2 K^–4)

	Acknowledgments

 
We thank Marilyn Banta for the use of her laboratory to take thermal images of the kangaroo rat in her teaching collection, University of Northern Colorado IACAUC protocol 0305 and Colorado Division of Wildlife Scientific Collecting License 04-TR1014. Other thermal images were of semi-tame animals foraging on spilled food in public campgrounds. Snake anatomy studies (Fig. 1) were done by S. Colayori under Indiana State University IACAUC protocol 2-10-2006:GSB/SEC, and were supported in part by a grant from the Indiana Academy of Sciences. NSF Grant 99-70209 provided the thermal imager, and Indiana State University provided general support.

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