JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 107, NO. B1, 10.1029/2000JB000015, 2002

4. Data Analysis

4.1. Image Processing

[12]   ALISS images were processed using two image processing packages: Image Reduction and Analysis Facility (IRAF) distributed by the National Optical Astronomy Observatories, and Interactive Data Language (IDL) distributed by Research Systems, Inc. A number of corrections must be made to remove additive and multiplicative systematic errors from the images (discussed in detail by Tyson [1986, 1990]) to perform accurate photometry. The image reduction steps are as follows:

  1. Remove DC bias level. Determined from a 20-column overscan strip (20 more columns are read than exist on the CCD array).

  2. Subtract bias structure. A fixed pattern associated with the CCD; obtained by averaging together a number of zero-second exposures.

  3. Subtract dark charge. Thermal signal built up on the CCD without external illumination, obtained by averaging together a number of closed-shutter, 5-min exposures.

  4. Median average multiple vent images to reduce noise. The standard deviation (sigma) for one pixel varied from ~0.01 in the background (~0.01 counts s-1 signal) to ~0.7 in the source area (maximum signal of ~1–3 counts s-1)

  5. Divide by flat field to correct for pixel-to-pixel variations. A flat-field image is made by imaging an evenly illuminated surface; these images were obtained on deck prior to each dive. During the image processing of the vent images the flat-field correction (dividing the vent image by the flat field) was made on a tile-by-tile basis.

[13]   Once the vent images were processed as described above, a source mask and complementary background mask were created using the channel with the highest signal-to-noise ratio (typically, the 870-nm filter) to isolate the area of light emission from the background. The same mask was applied to all 18 channels and count rates (minus the background levels scaled to the number of pixels in the source mask) were calculated for all filters. These values were divided by the source area giving the detected count rate at the ALISS CCD for each filter in counts cm-2 s-1. Analyses of specific parts of the plume were performed by limiting the source mask to a certain region, or to intensities within a specific range (i.e., from 0 to 100% of the intensity values measured). The light observed in the 870-nm channel was assumed to be dominated by thermal radiation. Thus variation in light intensity in this band can be used to indicate variation in temperature. In analyzing the spectrum of black smoker light we isolated portions of the source area into four quartiles based on intensity (or temperature): the 75–100 percentile region being the brightest/hottest quartile of the pixels and the 0–25 percentile region being the darkest/coolest quartile of the pixels.

4.2. Attenuation

Thumbnail link to Figure 4Figure 4.  Attenuation coefficients of water and seawater. The literature values [Hale and Querry, 1973; Jerlov, 1968; Kou et al., 1993; Pope and Fry, 1997; Smith and Baker, 1981] are consistent at long wavelengths and show variation at short wavelengths. The dark line indicates the values used to process ALISS data [from Smith and Baker, 1981; Kou et al. [1993], and modified for temperature as described by Pegau et al. [1997]). The visible region of the spectrum is from 350 to 750 nm.

[14]   Since light emitted at hydrothermal vents travels through 50 cm of water before reaching the ALISS camera, attenuation of light in water is an important optical property that must be included when analyzing data. Attenuation due to either absorption or scattering is exponential with distance and is characterized by a wavelength-dependent attenuation coefficient. This wavelength dependence confines much of ocean optical research to the visible region of the spectrum where light is attenuated the least. A summary of attenuation coefficients found in the literature is shown in Figure 4. Shoulders and peaks are present in the visible and near infrared regions of the attenuation spectrum at overtones of the O-H vibrational frequencies.

[15]   A number of scientists have experimentally determined the attenuation coefficients of both pure water and seawater [e.g., Curcio and Petty, 1951; Hale and Querry, 1973; Pope and Fry, 1997; Smith and Baker, 1981; Sullivan, 1963]. In most cases, the water used in these experiments was filtered to remove particulate matter which causes scattering. An attempt was made to measure the attenuation of water in the vent environment using the ALISS camera. This proved to be difficult due to the large bandwidth of the filters and sidelobe leakage. Because of the rapid change in attenuation with wavelength, a resolution of 10 nm is preferred, which cannot be obtained by ALISS's 50- and 100-nm bandwidth filters. Therefore the attenuation coefficients used for analyses of ALISS data are taken from Smith and Baker [1981] (seawater at 20°C) for wavelengths <700 nm and Kou et al. [1993] (pure water at 22°C) for the 700–1000 nm range. These values were modified to account for the differences in temperature and salinity as described by Pegau et al. [1997]. Smith and Baker's [1981] experiments used filtered seawater to remove the effects of scattering. Rayleigh scattering by particles smaller than the wavelength of light selectively scatter shorter wavelengths more than long wavelengths (i.e., the visible region is more likely to be affected by scattering than the infrared). Given the presence of particulate matter in the vent environment, the attenuation is probably higher than the literature values. However, given the low coefficient values in the visible region (10-3 to 10-4 cm-1) and the distance through which ALISS is imaging (50 cm), this has very little effect. The attenuation curve used in the ALISS calculations is shown by the solid line in Figure 4.

4.3. Inversion Method

Thumbnail link to Figure 5Figure 5.  The 450-nm filter curve and blackbody transmission through filter. (a) Effective aperture of ALISS through the 450-nm filter determined from calibration. (b) Synthetic photon flux (350°C blackbody with 103 photons cm-2 s-1 sr-1 added at all wavelengths) shown by the dashed line. After passing through 50 cm of water, the photon flux is attenuated as shown by the shaded line. Light that passes through the ALISS optics is shown by the solid line. Significant leakage occurs at long wavelengths (750–950 nm).

[16]   The photon flux from a vent is the number of photons emitted at the source per unit area per unit time per unit solid angle. This photon flux is attenuated as it travels through seawater and the ALISS optics, and is integrated over each filter, resulting in a count rate for each channel:

Equation 1

where Fluxvent is the photon flux at the vent in photons cm-2 s-1 sr-1, Omega is the solid angle subtended by the camera (i.e., the area of the entrance pupil of the camera divided by the square of the camera-vent distance, x2) in steradians and is 4.5 × 10-5 sr for each lens at 50 cm, kappa is the attenuation coefficient of seawater in cm-1 (Figure 4), TALISS is the transmission through the ALISS optics, QE is the quantum efficiency of the CCD (i.e., the number of electrons produced by an incident photon), CRALISS is the count rate measured by ALISS in counts cm-2 s-1, and the gain of the camera is 6.1 electrons count-1. The effective aperture (Aeff) of the camera (determined by calibration) includes the entrance pupil, the transmission through the ALISS optics (pressure window, filters, and lenses), and the QE of the CCD. Thus (1) can be written as

Equation 2

Our goal is to backward continue the ALISS data from the CCD (hereinafter referred to as “count rate”) to the vent to determine the photon flux at the vent orifice (hereinafter referred to as simply “photon flux”). Backward continuation becomes unstable due to the exponential factor in the equation; small errors are greatly expanded at long wavelengths during backward continuation. Additionally, the light transmitted through a filter is not entirely confined to the specified passband due to sidelobe leakage. For example, the 450-nm filter has a transmission of ~75% in the passband (400–500 nm) while outside of the passband the transmission is reduced by 4 orders of magnitude (Figure 5a). When observing a 350°C blackbody radiator, the photon flux at long wavelengths (>700 nm) is more than 4 orders of magnitude greater than the flux at 450 nm. Thus leakage occurs because the long-wavelength emission cannot be suppressed to insignificant levels with respect to the short-wavelength emission (Figure 5b). The attenuation coefficient is wavelength-dependent and increases significantly from 450 to 950 nm. Without being able to separate the flux by wavelength, an appropriate attenuation value cannot be determined to backward continue the data on a filter by filter basis (the light emission and attenuation coefficients can vary greatly over the 100-nm filter bandwidth). This problem affects all filters to some extent. Therefore an inversion routine is necessary to translate the ALISS data from integrated count rates at the CCD to continuous photon flux at the vent.

[17]   Inversion of data does not result in a unique solution. A number of possible models can fit the observed data to a given degree of tolerance. Therefore some method must be used to restrict the outcome to a range of models that have physical significance or are based on a priori information or constraints. This approach originated with Tikhonov [1963a, 1963b] (see also Franklin [1970] for a more general treatment) and has been adopted widely for geophysical inversion. For example, Constable et al. [1987] and Smith and Booker [1988] applied regularization to the inversion of magnetotelluric data by seeking the smoothest model consistent with a given set of data.

[18]   Before discussing the inversion, we will describe the simpler case of the forward model:

Equation 3

where d is a set of M data points, F is the forward functional (approximated as an M × N matrix), and m is a model that is N long. In our case, m is the photon flux at the vent (Fluxvent) (in 10-nm increments from 400 to 1040 nm); F describes how the photon flux is attenuated through seawater and the ALISS optics (e-kappax (Aeff/x2)) every 10 nm from 400 to 1040 nm; and d is the resulting data (CRALISS Gain) summed over each filter.

[19]   We define a roughness parameter as the integrated square of the first derivative with respect to wavelength:

Equation 4

where R1 is the first derivative roughness, m is the model, and lambda is wavelength. The inversion algorithm uses a series of iterations to search for the smoothest possible model (m) that fits the data (d) with uncertainty (sigma) to within a chosen misfit (X2). The misfit is expressed as

Equation 5

where W is a diagonal M× M weight matrix

Equation 6

and parallels denote the Euclidean norm. For ALISS data the uncertainty (sigma) in the data is due to noise in the camera system and uncertainty in the actual camera-vent distance. Camera noise is dominant at the shorter wavelengths and is ~25% of the signal. At long wavelengths, uncertainty in the camera-vent distance is dominant. At ~870 nm, where the highest signal is observed, a 5–10 cm error in distance results in a 22–49% error in count rate. Therefore we define an uncertainty of 25% for all data points. Because this uncertainty cannot be better constrained, the misfit that can be achieved is limited.

[20]   It may seem odd to seek the smoothest model, when it is possible for sharp discontinuities to occur in the data (e.g., emission bands). However, because of the width of the ALISS filters (nominally 100 nm), the camera is not capable of resolving such peaks. Thus the smoothed model is able to show regions of excess emission that can be detected given the resolution of the camera.

Thumbnail link to Figure 6Figure 6.  Inversion of ALISS data from P Vent (9°N EPR). (a) ALISS data (shaded dots) with 25% uncertainty error bars are compared to the response of the inversion model (solid circles) shown in Figure 6b. The high data value from the 450-nm filter with respect to the 500-nm filter is due to long-wavelength leakage (see Figure 5). (b) Inversion of the ALISS data (shaded line) is compared to a 340°C blackbody with an emissivity of 0.3. The inversion model tends to flatten at either end (400–500 and 900–1000 nm) and cannot resolve values below the detection level of the ALISS camera (dash-dotted line).

[21]   An example of ALISS data and an inversion model is shown in Figure 6. ALISS data (i.e., the count rate detected by the camera at a distance of 50 cm from the vent) from P vent (9°N EPR) are plotted as shaded dots in Figure 6a. The count rates tend to increase with increasing wavelength as expected for a thermal source. The decrease in count rate above 870 nm is due to the increasing significance of attenuation in that region (see Figure 4). The inversion technique described above was used to determine a photon flux at the vent from the count rates recorded by the ALISS camera. The inversion model (photon flux) is plotted as a solid line in Figure 6b and is compared to a theoretical thermal source (340°C blackbody of emissivity of 0.3). Flattening occurs at the extreme ends of the model due to the lack of constraints outside of the 400–1040 nm region and the restriction on the inversion method to generate the smoothest (i.e., flattest) possible model. The center portion of the model corresponds well to a blackbody flux. The response of the inversion model (i.e., the predicted ALISS count rate resulting from running the inversion model through the forward functional) plotted as open circles in Figure 6a correspond well to the actual ALISS data.

Thumbnail link to Figure 7Figure 7.  Inversion of synthetic data. (a) A synthetic flux (330°C blackbody with an excess flux of 104 photons cm-2 s-1 sr-1 in 500–550 nm region) run through the forward functional to generate synthetic ALISS data (shown in Figure 7b with 25% error bars). The data were then inverted (shaded dotted line) and compared to the original synthetic flux (solid line) (Figure 7a). The inversion successfully returns the blackbody curve, and the excess flux in the visible region is well approximated by the inversion program. (b) Comparison of the synthetic data (diamonds) and inversion response (shaded dots).

[22]   While we know that thermal radiation is occurring at vents, we are also looking for excess light in the visible wavelengths. In order to test the ability of the inversion program to resolve this, a synthetic data set was created. A synthetic light curve (a 330°C blackbody flux with an excess intensity of 104 photons cm-2 s-1 sr-1 from 500 to 550 nm (Figure 7a)) was run through the forward functional to generate synthetic data (Figure 7b). The synthetic data were inverted and compared to the original synthetic light curve. The inversion response (shaded dots) fits the synthetic data (open circles) well (Figure 7b). The inversion model is smoother than the synthetic curve but is able to retrieve the excess flux in the 500–550 nm region.

AGU

Citation: White, S. N., A. D. Chave, and G. T. Reynolds, Investigations of ambient light emission at deep-sea hydrothermal vents, J. Geophys. Res., 107(B1), 10.1029/2000JB000015, 2002.