Light reflected by an object and received on a photoreceptor produces a signal response , which is a function of the spectral sensitivity of the receptor (S), the spectral power distribution of the illumination (E) and the reflectance spectrum (R) of the illuminated object expressed as:(1)Equation 1 is the core of most colourimetric equations replacing (S) by a function describing the spectral sensitivity of one of the three different cone classes in the human visual system [42]. Equation 1 can also be applied to model photon catches by non-human visual systems [34], [43].

When Equation 1 is applied to model the response of a CCD or CMOS digital camera, the camera response () is expressed in terms of pixel intensity levels. At any given pixel, the camera response is a function of: the sensor response (), the intensity of the signal (I), the selected exposure parameters (H), including selected aperture, integration time, image magnification and sensor size [44], and the amplification (gain) of the sensor response (G); a nontrivial function of I and H, which is unique to each camera model and colour channel [26], [31]. In the case of an RGB device this relation is expressed as:(2)for each colour channel i.

In digital cameras for technical use, G is a constant, thus the camera response is linearly related to the intensity of the signal, which in turn is controlled by the exposure settings. Hence we can write Equation 2 as: . However, more typically, G takes a non-linear form in RGB digital cameras producing camera responses () which are not lineary related to signal intensity [44]. Moreover, consumer-level camera responses are also subject to other non-linear operations, commonly referred to as ‘gamma correction’ [26]. These aim to improve the aesthetic appearance of the images when displayed on computer monitors and/or to increase the effective dynamic range of the camera to human perception [27], further contributing to the non-linear behaviour of [26], [27]. Therefore, the parameter G in Equation 2 models most of the non-linear operations introduced into the RGB camera response [31].

When employing a digital camera to accurately quantify a visual signal by means of Equation 2, it is essential to recover the linear sensor response as a first step prior to any further analysis. This is achieved by finding a non-linear mathematical expression describing the G function and inverting it, implementing either analytical or optimisation methods [26], [31]. However, different camera models may have different transfer functions and the precise values of the coefficients describing the transfer function for a particular camera must be found experimentally through a characterisation and linearisation exercise. Details of different camera characterisation methodologies and fitting functions are available elsewhere (e.g. [31]), along with a precise mathematical formulation of the procedure.

We used a typical, consumer-level digital single lens reflex (DSLR) camera: a Canon D40 (Canon Inc., Japan) and a Fuji S3 UVIR (Fujifilm Corp, USA) DSLR modified for ultraviolet and infrared imaging to record flower reflection within a spectral interval from about 320 to 710 nm. Canon Macro Lite (Canon Inc., Japan) and Nikon Speedlight SB-14 (Nikon Corp., Japan) electronic flash units were employed as illumination due to the close resemblance of their spectral output to that of daylight [45]. The Speedlight unit was modified by an expert camera technician (Beyond Visible, USA) to increase its UV output ( nm), thus facilitating the use of this unit in the field. To prevent radiation longer than about 395 nm from reaching the sensor of the Fuji S3 UVIR camera, a Baader U filter (Company Seven, USA) was fitted in front of a Micro Nikkor 105 quartz lens by means of a filter holder. The use of quartz optics ensured the transmission of ultraviolet radiation down to about 200 nm [33]. Flower visual signals within the visible region of the spectrum ( nm) were recorded with the Canon D40 camera. The camera was equipped with a Canon 100 mm Electro-Focus (EF) lens (Canon Inc., Japan) which was equipped with a skylight filter (Hoya, Philippines) for cutting-off radiation below about 390 nm.

Characterisation methods and reconstructed spectral sensitivity curves for the Fuji S3 UVIR camera have been published elsewhere [33]. This methodology was employed here to reconstruct the spectral sensitivity curves of the red, green and blue channels of the Canon 40D digital camera (Figure 1). Reconstructed linear spectral sensitivity functions of the two cameras were modelled fitting a Gaussian function including either one or two exponential terms:

or(3)for the colour channel available on each camera. We chose the form of Equation 3 which best fits the sensitivity data for each colour channel based on the statistical significance of each individual parameter. Mean values and 95% confidence intervals for the obtained coefficients are provided in Table 1.

We recorded images in the visible and ultraviolet region of the spectrum from flowering plants belonging to the species: Oxalis pes-caprae, Goodenia ovata, Geranium sp., Malus domesticus, Gazania rigens, Freesia laxa, Sonchus oleraceus, and Eremophila macculata, which were available at the campus of Monash University (Clayton, Victoria, Australia), during mid-spring of 2013. The use of electronic flash units with known spectral power distributions as irradiation sources reduced potential effects of variations in ambient illumination. Images were always recorded in a shadowed area, and exposure was set to minimise the contribution of ambient light to each exposure.

Flowers were first recorded using the ultraviolet-sensitive camera and immediately after, with the camera sensitive to visible radiation. Images were recorded with magnification ratios between 1∶3 and 1∶7 as indicated by the size scale included on each panel of Figures 2 and 3. ISO was set at 200 on both cameras. To account for image registration, the same image magnification ratio was fixed on both the Nikon and Canon lenses prior to photographing each one of the flower samples. Focus was achieved in all images by carefully positioning each one of the cameras.

Three different calibration targets were included on each frame as reference for setting an adequate photographic exposure: i) a NIST traceable white reflectance standard for spectrophotometry (Ocean Optics, USA), ii) a grey achromatic target made of barium sulphate and activated charcoal uniformly reflecting about 33% of incident radiation within a 300 to 400 nm spectral interval [46], (Figure 4 panel I), and iii) the ‘white’ target of a Passport Colour Checker (Xrite, USA) uniformly reflecting about 95% of visible radiation within a 400 to 710 nm interval [47].

Images were recorded on the native RAW format for each camera: CR2 for the Canon camera and RAF for the Fuji S3 UVIR camera. RAW image files were processed employing the Camera Raw plug-in v.6.3 (Adobe, Inc., USA) for Photoshop CS5 (Adobe, Inc,. USA). Processed RAW files were encoded into uncompressed 8-bit TIFF files using the same software package, and subsequently linearised using custom codes written for Matlab release 2012b (The Mathworks, USA) [31]. Matlab m-code is available from the authors by request.

Exposure of each individual image was standardised based on the camera response predicted by Equation 1. For the exposure calculations we used reflectance spectra corresponding to the achromatic calibration targets. The CIE daylight illuminant at 6500 K (D65) was selected as reference illumination (E) for all calculations. Spectral power distribution for the selected illuminant was calculated following the CIE method [42].

White balance was set at 5100 K for the RGB images recorded with the Canon camera and left as interpreted by the ‘daylight’ setting available on the Fuji S3 UVIR camera. All images were encoded in the Adobe RGB 1998 colour space [48].

Processed TIFF files were linearised using look-up tables (LUT) constructed by inverting a biexponential function of the form:(4)which describes a readily-applicable version of the function for the different transfer functions for each one of the colour channels of both cameras [31]. For the particular case of the i = ‘red’ UV-sensitive channel of the Fuji S3 UVIR, a function with a single exponential term of the form:(5)with coefficients and 95% confidence bounds: and was selected to fit the transfer function. However, functions like Equation 5 do not necessarily fit transfer functions for other colour channels and/or camera models as is the case with the Canon 40D, whose transfer functions are only accurately fitted by including a second exponential term as in Equation 4 [31].

In order to recover reflectance rather than radiance values from linear RGB camera responses, the linear responses were divided by the exposure value required to obtain a maximum camera response value equal to 245 intensity levels. Selecting a maximum camera response value below the maximum value attainable for an 8-bit colour space, i.e. 256 pixel intensity levels, ensured that average camera responses did not include overexposed (‘clipped’) pixel data points [26]. Total irradiance (intensity) values required to obtain for each colour were: mol, mol, mol, for the red, green and blue channels of the Canon camera and mol for the red UV-sensitive channel of the Fuji S3 UVIR camera. Exposure was calibrated individually for each channel to avoid using software-based white balancing algorithms.

Spectral reflectance data from the selected flower species were recorded using an Ocean Optics spectrophotometer (Ocean Optics, USA) equipped with a PX-2 pulsed xenon light source (Ocean Optics, USA). A UV-reflecting white standard from the same manufacturer was used for calibration. To account for the multiple colours displayed by the selected flowers, we measured reflectance from three different points along the major axis of each petal [19], [22]. A larger spectrophotometric sample, including 15 pseudo-randomly allocated points, was taken from a Goodenia ovata flower to better gauge the amount of chromatic variability. The increased sampling area enclosed the three bottom petals of the flower (Figure 4, panel b).

Camera responses () predicted by Equation 1 were compared against values obtained from two different image sampling schemes: i) point sampling and ii) local variability to a) estimate the magnitude of the differences expected between the photographic and spectrophotometric methods and, b) assess the amount of chromatic variability unaccounted for when point samples rather than larger areas are used to model the visual appearance of flowers.

For the point sampling experiment, 1515 pixel areas were sampled from linearised images recorded using visible (400 to 710 nm), and UV (320 to 395 nm) radiation reaching the sensor of the Canon and Fuji cameras respectively. For the local variability experiment, three different square pixel areas were pseudo-randomly selected from either a 43 (sampling scheme A), or a 62 (sampling scheme B) square grid. The sampling scheme was selected so that a single petal of each one of the measured species was totally enclosed by the grid as depicted in Figure 5.

Accuracy of the linearisation procedure was tested by comparing the recovered normalised linear camera responses obtained from the six achromatic samples present in the X-Rite Colour Checker passport against their reflectance values measured with a standard spectrophotometer (Figure 6).

Reflectance values obtained from the linear camera responses did not differ from those obtained by spectrophotometric readings for the achromatic samples reflecting from 9% up to about 95% of incident irradiation . Reflectance values predicted from linear camera responses for the ‘black’ swatch, reflecting 3.10% of the incident radiation, did significantly differ from data published for this sample (Figure 3, panel a). For the non-linearised camera responses, all but those responses corresponding to the brightest achromatic sample were significantly different from the responses predicted from spectrophotometric readings (Figure 3, panel b).

Images representing linear camera responses were always darker than their unprocessed, non-linear counterparts (Figure 6 image stripes and Figures 2–3). Reduced brightness in linearised image results from displacing the compressed camera responses at high irradiance levels (Figure 6, panel b) towards the middle region of the transfer curve (Figure 6, panel a).

Images representing linear camera responses in the visible and UV spectral regions were reconstructed from floral specimens of the species: Oxalis pes-caprae, Goodenia ovata, Gazania rigens, Geranium sp., Malus domesticus, Freesia laxa, Eremophila macculata and Sonchus oleraceus (Figures 2 and 3). On each image an achromatic, spectrally-flat standard was included as an internal control for exposure calibration and potential variations in colour that might have arisen as a result of the independent processing of each colour channel of the different images.

Total reflectance as measured by the camera was obtained from three pixel² sampling areas located at the tip, middle and base of a single petal of each one of the selected species, and from wider sampling areas (mean =  pixel²), representing wider areas than those covered by the spectrophotometer probe.

In most of the cases the two methods differed in the magnitude of the mean total reflectance measured for the flower samples across the different spectral bands (Figure 7), but they were not statistically different for the achromatic calibration standard (). Moreover, the magnitude of the standard deviation from the intensity values obtained from linear camera responses was higher than that corresponding to the measured reflectance spectra (Figure 7). These results suggested that the differences observed in intensity values between the two methods are produced by the intrinsic local spatial variability of the samples rather than an inaccurate recovery of total reflectance from RGB responses.

To obtain a better understanding of the nature of the observed differences, we performed a new comparison between the total reflectance obtained from the two methods by sampling a wider area of Goodenia ovata incorporating the three lower petals of the flower and including the UV-reflective marks (Figure 4, panels a and b). For this measurement, the number of samples measured with the spectrophotometer was increased to 15 and the image sampling area was increased to cover an area of 2500 pixels² matching that sampled with the spectrophotometer.

Total reflectance calculated from spectral data and recovered by the camera system is graphically summarised in Figure 4 panel c, along with the measurements obtained from the grey calibration standard. Consistent with data in Figure 3, total reflectance values obtained from spectrophotometry and from linear camera responses significantly differ from one another for the red, green and blue channels of the Canon 40D (Wilcoxon rank sum test , , ); however, we did not find significant differences in the amount of total reflected UV measured by the two methods ().

Results from the last experiment suggest that chromatic variability is not equal across the different spectral bands but higher in some spectral regions. In the case of Goodenia ovata, the lowest variability was observed in the UV-sensitive channel and highest in the long wavelength (red) channel (Figure 4, panel I). Distributions of the total brightness values for each colour channel are summarised in Figure 8. Total reflectance values recovered by all but the red channel of the Canon 40D camera were found to be significantly non-normal at an level of 0.05 (Shapiro-Wilk , , , ).

Naturally occurring samples typically present wide variations in their total reflectance values across two dimensions (Figure 4). This variation arises from intrinsic characteristics of each sample such as pattern texture, shape and volume (Figure 2–3). These characteristics are often overlooked, probably because of the difficulty of measuring them accurately using point samples [49], [50]. Yet measuring this variation is potentially of biological importance since it provides insight into the challenges faced by a pollinator’s visual system for detecting and correctly discriminating target flowers in visually complex environments. Our finding is consistent with a recent report that spectral measurements from different flowers of the same species often show wide variability in spectral signals to pollinators [19].

Misrepresentation of visual complexity when using spectrophotometry may arise as point samples can not always represent potential variation in shape, pigmentation and/or lighting effects for a given flower. For example, the ‘white’ flower of Malus domesticus has a complex three dimensional structure resulting in self-shading effects that the visual system of a pollinator would have to deal with (Figure 3). A spectrophotometer measuring colour at an ideal angle would potentially underestimate spectral signal variability (Figure 7). Thus the variability in the different systems reported here should be taken as a representation of the likely differences in signal processing attainable with a typical spectrophotometer set-up and a digital camera system with a limited number of spectral bands (n = 4) and staged in a consistent manner. This can be clearly seen by comparing the variability of colour signals within boxes of Figure 7, which illustrate the greater variation in signal in Geranium sp. than in Oxalis pes-caprae.

The appearance of flowers may also be influenced by various optical effects like iridescence [51], [52] produced by microscopic structures acting as photonic crystals or diffraction gratings [53]. Presence of iridescence in a petal or other plant material may increase the intensity of a given colour signal compared to a pigment-based signal [52], [53], which may lead to overexposed or clipped RGB values. The presence of these signals will undoubtedly introduce artefacts in the estimation of the signal’s radiance by means of linear camera responses [26]. This is one reason for employing specialised methods for the measurement of these particular signals [53], [54].

Variability on any given flower is not only limited to fluctuations in total brightness across the sample, but it is also manifested within the different spectral bands (Figure 8). This chromatic variability is represented by discrepancies in the shape of the distributions of the linear pixel intensity values within the UV, blue, green and red spectral bands, and are likely produced by the presence of pattern elements of varying hue and intensity within a petal. For instance, the highest chromatic variability in Goodenia ovata was observed in the red and green colour channels, corresponding to the (human-perceived) yellow pattern, whilst the lowest variability corresponded to the plain UV-reflective marks (Figure 4).

Other sources of spatial variability may also include variations in the recorded reflectance values produced by volume scattering, which is characteristic of leaves, fine plant structures and small dust particles [55]. Although the effect of volumetric scattering has been studied for radar imagery and other remote sensing techniques [55], [56], its potential effects on measurements using purely optical radiation remains untested. Future work could address this issue, in particular, when using infrared digital imaging.

Lack of uniformity in the brightness values through the sampled area and the selected spectral bands, suggests that visual signals produced by flowers are complex and should be regarded as multidimensional entities where each dimension potentially represents a different source of variability.

In spite of the advantages of digital photography to measure spectral and spatial variation in flower signals, recovered linear camera responses are limited to: i) the uncertainties associated with the implementation of a biexponential linearisation equation, ii) the colour gamut covered by the camera’s own colour space and iii) the spectral interval spanned by sensitivity curves of the colour channels available in the camera system.

The uncertainty associated with the recovered linear response is not uniform along the different values of the camera response [31], being particularly high at values corresponding to less than about 9% of incident radiation (Figure 6). Below this point camera responses are dominated by noise and are very likely described by a different relationship than camera responses at higher irradiance levels [26], [57].

In spite of being qualitatively close to the perceived aspect of a flower by a human observer, camera responses corresponding to highly saturated, human-perceived yellow and orange colours, such as those displayed by Gazania rigens and Sonchus oleraceus, do not correspond to those expected from their reflectance spectra; in other words, camera responses are not radiometrically faithful for these hues. This problem arises due to the smaller colour space reproduced by digital devices compared to animal colour spaces and that of a human as described by the CIE observer [48], [58].

It is likely that in order to reproduce a colour perceptually similar to that observed in highly saturated yellow samples, the inbound camera software increases the red channel response above the physical reflectance value for these samples whilst lowering the response of the green channel (Figures 2–3 and 7). As a consequence, linear camera responses corresponding to these hues are likely to be inaccurate. An efficient way to evaluate this potential problem is by measuring the RGB values in the non-linear image. Values corresponding to the red channel for the sample should never be above those reported for an achromatic calibration target reflecting more than about 90% incident irradiation. However with the current data it is not possible to identify the precise mechanism by which this correction is made, or if it involves a linear or non-linear transformation. A better understanding of the way the camera software deals with these colour samples remains an open field for research, and could be of value for other image processing tasks involving linear camera responses such as spectral reconstruction [59].

Finally, caution is suggested when interpolating linear camera responses to other trichromatic colour spaces, including CIE uniform colour spaces such as the CIE Lab, as the spectral tuning of the two systems may not completely overlap [60]. For example, a direct mapping between the Canon 40D camera employed here and any colour space based on human vision is very likely to be inaccurate as the spectral tuning of the respective systems differs (Figure 1). This limits the number of visual signals that can be accurately mapped to those whose spectral signature matches the spectral interval shared by the sensitivity functions of the two systems predicted by Equation 1, and has motivated the development of methodologies for spectral reconstruction from RGB camera responses [27], [60]. Future work should aim to obtain a better understanding of mappings between camera colour space and those of different animal observers through carefully designed camera characterisation experiments.