Laboratory Calibration in Distilled Water and Seawater of an Oceanographic Multichannel Interferometer-Refractometer (2024)

a. Unique advantages

The utility of index of refraction measurements for determining the density of seawater have long been recognized, but their value in other areas is also becoming apparent. For example, developing an alternate equation of state (AEOS) that uses the index instead of the electrical conductivity of seawater will shed more light on the role of pressure and the ratio of salts in determining density. The index of refraction (speed of light in the medium) is determined by the number of electrons the wave perturbs in its path, whereas the electrical conductivity is determined by the number and mobility of ions in solution. The former is more nearly related to the molecular weight and is useful in fresh as well as salt water; the latter is related to the ionic valence/weight ratio. A comparison of these calculated “densities” could fine-tune both EOSs, as well as be a measure of the ratio of salts as a water mass property.

A second application is in the measurement of ocean microstructure, which requires a fast, single-probe, density instrument (Belyayev et. al. 1979; R. Schmitt, 1995, personal communication). The gradient of the index here can be independent of temperature and pressure and thus proportional to the gradient of density. Also, the small sample size of the refractometer may make possible the resolution of the smallest scales of salinity variation in the ocean, which, because of its lower diffusivity, are much smaller than the scales of temperature variability. The measurement of the effects of evaporation on density in the salinity boundary layer (less than 1 mm from free surface) can best be accomplished with the single probe of the index measurement (Federov et. al. 1979).

The index measurement can also be developed for use as a long-term, stable surface density and salinograph, particularly in the Arctic where the index and density is only a very weak function of temperature. The measurement principle is less sensitive to fouling and freezing than is the conductivity approach. Long-term surface salinity records at high latitudes are of importance to global climate change studies, and density measurements are of use in ballasting problems.

And finally, knowledge of the turbulent index field in the ocean is itself necessary toward a better understanding of underwater coherent laser communications; the strength of the index fluctuations determines the maximum beam diameter (coherence diameter) and ultimate laser range.

b. History of refractometry in physical oceanography

The first recorded instance of the use of the index of refraction measurement to determine seawater density occurred in 1877. Hilgard of the U.S. Coastal Survey Office converted his sextant to a hollow prism, minimum-deviation refractometer (1877); this was to replace the “bobbing hydrometers” then used at sea to measure density. The first successful application of optical interferometry for the measurement of the index of refraction of seawater in situ was done at the end of the 1970s. Dr. V. L. Vlasov of the P. P. Shirshov Institute of Oceanology (Moscow, Russia) developed a laser interferometric refractometer for use in oceanography. In 1977 during cruise 19 of the R/V Dimitry Mendeleev, Drs. Vlasov, R. V. Ozmidov, and V. S. Belyaev for the first time used the technique to measure thevertical fine structure of density in the ocean directly through the measurement of the index of refraction (Belyaev et al. 1979). From this early work came the Lamina-2 interferometer-refractometer that is discussed in this paper.

Soon after the 1979 Belyaev paper, Dr. G. Seaver of SeaLite Engineering began developing a critical wavelength refractometer (CWR) to measure the absolute index of refraction of seawater to 4 × 10⁻⁶ (1986, 1987); to implement this, he also began developing an equation of state for seawater involving the index of refraction, temperature, pressure, and salinity (1985, 1990). Also, Mahrt (1982, 1984, 1988) at the University of Kiel, Germany, developed both a laboratory interferometer-refractometer and an in situ profiling Abbé refractometer during the 1980s; the laboratory model had a reported accuracy in the index of refraction of approximately 1 × 10⁻⁶. Before this, the vertical density stratification was determined by calculations based upon the vertical distribution of the salinity S, temperature T, and pressure P obtained by CTD probes, which produced “spiking” in the thermocline salinity profiles.

Before 1977, interferometers were used only under laboratory conditions in thermostated and vibration-protected chambers (Stanley 1970). Two goals were achieved during the Mendeleev cruise of 1977: 1) the measurement of the density fine structure was accomplished without the false inversions customarily seen with traditional sensors; 2) the high sensitivity and accuracy of the interferometric method was successfully applied to the investigation of physical processes in the ocean. This was made possible by the instrument’s immunity to environmental noise and the use of the method of phase photoheterodyne interferometry developed by Vlasov in 1959. This method of optical heterodyning was first developed by the American scientist L. Forest in 1957–58. However, his method only demonstrated the possibility of optical heterodynment, by analogy to heterodynment in the radio band, and did not resolve questions of precise phase determination in optics and the elimination of their inherent noise.

Finally, we note that the limiting accuracy at the moment in deriving salinity and density from the index comes from the uncertainty of the algorithm relating the index of refraction to salinity, density, and temperature (Millard and Seaver 1990). This accuracy is approximately 3 × 10⁻⁶ g cm⁻³ for distilled water and 20 × 10⁻⁶ g cm⁻³ for the oceanographic range of variables.

a. The principle

The immunity to environmental noise is achieved in the following way: light beams that form the two channels and, subsequently, the two systems of interferometric fringes, pass through the measuring interferometric arms via optical components (mirrors, beam splitters, beam couplers, etc.) attached to the same structural elements and with only a small distance (a few millimeters) separating them. Thus, all mechanical vibrations act in a similar manner on both interferometric fringes and do not result in any relative shift. Vibrations, therefore, do not influence the phase shift of the resultant electrical signals. Visual measurements of the shift of interferometric fringes in a conventional laboratory refractometer under normal environmental vibration are very difficult because of this fringe erosion.

The immunity to temperature-induced changes in the interferometer reference arm is achieved by a similar method. The same change in optical length occurs in both beams and is subtracted out when the photodetector’s electrical signals are combined. Specifically, the system of two optical windows in Fig. 1 (item 9) are positioned on the base in the form of steps, which are made from metals of different thermal coefficients of linear expansion, ε₁ and ε₂.

b. Sensitivity of the method

The position of the interferometric fringe with respect to the photodetector diaphram δα has some uncertainty to it, which is α₂. This is caused by destabilizing factors, such as vibration and temperature changes that produce drift and fluctuations of the fringes; this is in addition to the previously discussed environmental noise effects. Thus, systematic, periodic deviations from a linear fringe shift–phase shift relation frequently exist and appear as a random error in the relative fringe shift measurement. If a₁/a₂ = 0.01, the theoretical error is about 0.002 of an interferometric fringe; in laboratory experiments this error was observed to be 0.005 of a fringe (Vlasov and Medvedev 1972, 1975). Taking the value of 0.005, we obtain for the resolution, δn = 1.5 × 10⁻⁷; this is for an optical base length of l = 20 mm and a wavelength of 632.99 nm. Based upon this resolution, we can then calculate the resultant resolution for S, T, and P using the partial derivatives δS/δn = 0.5 × 10⁴ psu, δT/δn = 10⁴°C, both at 20°C, and δP/δn = 0.7 × 10⁶ db. The resolution, then, for S is 0.0007 psu, for T is 0.0015°C, and for P is 0.1 db.

However, for the Lamina-2 instrument, the limitation on resolution comes from the primitive technological nature of the phasometer used. It has a resolution of 1/32 of a fringe, which leads to a resolution of 1 × 10⁻⁶ in the index of refraction, of 0.005 psu in salinity, of 0.010°C in temperature, and 0.7 db in pressure. This is approaching the resolution of modern CTDs; the difference is that CTDs have reached the limit of theirtechnology, whereas the interferometer refractometer has not. For example, the phasometer can easily be improved to a resolution of 0.01 fringe; other improvements can also be made as indicated below. We note that the first submersible interferometric refractometer (Belyaev et al. 1979), constructed on the basis of the Mikelson scheme, had an optical base length of 5 mm and a phase resolution of 0.1 fringe, leading to a resolution in index of 13 × 10⁻⁶.

c. Operation of the optical multichannel probe Lamina-2

d. Prior experimental results of Lamina-2 in the ocean

In Fig. 2 the vertical fine structure of the index of refraction, temperature, and salinity taken by Lamina-2 in the Atlantic Ocean is shown. These measurements were made during cruise 14 of the R/V Professor Sergey Dorofeyev at station N100 in January 1990. From a comparison of the salinity and temperature profiles with that of the index of refraction (which closely follows the shape of density), we can see that the index of refraction from Lamina-2 gives us a “temperature minus salinity” view of the ocean and demonstrates the dynamical fine structure with depth. For example, the salinity and temperature inversions do not result in inversions or spikes in the index or density fields. The same is true of the smaller inversions seen in the main thermocline. There we see the characteristic steplike structure in n, S, and T, not the false spikes that are often seen in the calculated salinities and densities profiles from CTD measurements.

The results obtained from Lamina-2 on this cruise were impressive and suggest that the optical autocompensation scheme of Lamina-2 worked well; interferometers traditionally suffer from temperature and vibration effects on thereference arm in the interference scheme and these must be corrected or compensated for. However, in reference to accuracy, the instrument had never been evaluated in a recognized international calibration facility; thus, the next step was to test Lamina-2 in a precise index of refraction calibration laboratory. In the fall of 1992 discussions began on having a workshop to evaluate and to calibrate Lamina-2 against temperature and salinity standards at atmospheric pressure. This workshop was held at the Woods Hole Oceanographic Institution and SeaLite Engineering from 17 September to 14 October 1993 and was run by Dr. Seaver, who was a guest investigator at WHOI at the time. The facilities and some of the equipment used during the workshop were subcontracted from WHOI; Lamina-2 and the distilled water calibration tank are shown in Fig. 3. A preliminary report on the workshop was issued in January 1994, which is available from NSF or SeaLite Engineering; the remainder of this paper is a formal discussion and evaluation of the results of that workshop.

a. Lamina-2 thermocompensation and temperature results

As the index is less sensitive to temperature than to salinity and density (it is a bad thermometer), the temperature channel is seen primarily as a diagnostic for autocompensation, index, and algorithm errors. A comparison in distilled water of the temperatures measured by Lamina-2, T_L, and by the OTM, T_otm, for the temperature range 23°–18°C (cooling) was made; the difference between them plotted against time is shown in Fig. 5. The mean difference is less than 0.04°C in the dynamical range, during cooling, and is nearly zero in the stationary regime when the temperature was constant; the stationary points are shown in Fig. 5 at times 0–400 s, 700 s, and 6100–6700 s. The maximum random deviations were 0.03°C under cooling and 0.01°C at a constant mean temperature. As the temperature change of the calibration tank was 3°C h⁻¹ (index change rate of 0.326 × 10⁻³ h⁻¹), the temperature response mismatch of the OTM and Lamina-2 is ruled out as the cause of this error; these time responses were 0.4 and 0.04 s, respectively. The above mean temperature difference is probably explained by the incompleteness of the temperature autocompensation scheme. This 0.04°C mean error translates into a 4 × 10⁻⁶ error in the index; this, as we will see in section 5b, is about the same as the mean error we found in the index of refraction measurement channel (see Fig. 7).

The above-mentioned random deviations are the result of electronic noise, as well as the spatial separation of the two temperature sensors (≈ 7 in.) and the turbulent nature of the bath. The random deviations in the stationary regime are less than the theoretical random errors previously reported for Lamina-2 by Vlasov et al. (1991). We note that, because the index of refraction is only weakly dependent upon temperature, it makes a poor thermometer and the random temperature error here represents a small (ppm) error in the index. The mean and random errors shown in Fig. 5 would be much worse without the automatic temperature compensation designed into Lamina-2. For this workshop the value of the fringe shifts with(aT) and without (faT) compensation was tabulated for the run of Fig. 5, and their difference is shown in Fig. 6. Switching on and switching off the compensation channel was done by a special software program developed specifically to process the data from Lamina-2 during the 1993 workshop. In an output file the following information was recorded:

1. time

2. aT, fringe shift in the temperature channel

3. aS, fringe shift in the salinity channel

4. aP, fringe shift in the pressure channel

5. aN, fringe shift in the index of refraction channel

6. dnT, index of refraction change in the temperature channel

7. dnS, index of refraction change in the salinity channel

8. dnP, index of refraction change in the pressure channel

9. dnN, index of refraction change in the seawater channel

10. T, temperature (°C)

11. S, salinity (‰)

12. P, pressure (db)

13. faT, fringe shift in the T channel without temperature compensation

14. faS, fringe shift in the S channel without temperature compensation

15. faP, fringe shift in the P channel without temperature compensation

16. faN, fringe shift in the N channel without temperature compensation

The switching on of the compensation channels corresponds to measurement of the difference in phase shift between two systems of interferometric fringes, as shown in Fig. 1. Switching off of the compensation channel corresponds to measurement of the difference in phase shift between one system of interferometric fringes and a reference electrical signal from a signal generator. This difference between aT and faT versus temperature is shown in Fig. 6.

From an inspection of Fig. 6 we see that the fringe shift error with no compensation is about one full fringe for a temperature run of 5°C. The curve has random noise of ±0.1 fringes in amplitude. A difference of one fringe corresponds to a systematic error in temperature of 0.3°C and 30 × 10⁻⁶ in the index of refraction. The random noise converts to ±0.03°C in temperature and ±3 × 10⁻⁶ in the index. So without temperature and vibration compensation the interferometric method would be unacceptable for use in oceanography. As was stated before, the systematic error is related to the optical base length change due to ambient temperature change. The random error is due to the ambient vibration level, as well as the instability of the phase difference between the electrical signal from the reference generator and from the photodetector. The reason for this latter instability relates to the imperfect electrical scheme of the digital, reversible phasometer, which we hope to improve in the future.

The degree of forcing of the autocompensation scheme that was experienced in the above calibration is comparable to the actual ocean environment in the case of vibrations. Lamina-2 was suspended in the calibration tank by a winch used to raise and lower it; there were heavy pumps in operation in the laboratory at the time and vigorous turbulent stirring of the calibration tank was in effect to remove spatial temperature gradients. However, in regards to the range of forcing in the temperature autocompensation case, the range was only 7°C over 3 h, which is only about 25% of that found in actual ocean profiling. The completeness of this compensation was discussed briefly in section 5a; there appears to be a lag in the temperature autocompensation that results in a 4 × 10⁻⁶ indexerror under a cooling rate of 3°C h⁻¹ (an index of refraction rate of 0.326 × 10⁻³ h⁻¹).

b. Lamina-2 index of refraction results and errors

The primary value of a refractometer in oceanography is to measure the index of refraction of seawater, and the calibration of this capability is the major result of this workshop. Following the autocompensation test of Lamina-2 in cooling from 23° to 18°C, the experiment was continued from 18° to 12° and then from 12° to 5°C in order to calibrate the instrument’s primary channel, the index of refraction of the distilled water itself. Figure 7 presents the difference between the Lamina-2 measurements of the index of refraction and that calculated by the SM algorithm (1990) using the OTM temperature during the cooling experiment from 23° to 5°C. The values of δn shown in Fig. 7 for 5° < T < 12°, unlike those for 12° < T < 23°, were averaged over 100 points or 8.5 s. For the range 12° < T < 23° the data was not averaged, but rather the last point in the set of 100 was taken, thus giving the same time step of 8.5 s. The standard deviation of the index over the full range from 5° to 23°C was 4.3 × 10⁻⁶, which is about three times the theoretical prediction.

Figure 7 actually shows three separate experiments: 5° < T < 12°, 12° < T < 18°, and 18° < T < 23°, and there was a pause between each segment. If the systematic error of Fig. 7 is also seen under pressure and other variations and it becomes possible to remove it, then we would be left with the random error. By averaging through 100 samples (or 8.5 s), as described in the previous section, we would then have an error of ±7 × 10⁻⁷, as indicated in the first segment of Fig. 7. This is consistent with the predictions on sensitivity and accuracy as discussed by Vlasov et al. (1991). We believe that some of the above systematic error is caused by the movement of the optical windows and would be eliminated with a new design. For example, Rossby (RAFOS floats), Seaver (CWR 1986), and others have developed techniques for direct metal-to-glass mating for underwater high pressure instrument design to remove any possibility of flexure.

c. Lamina-2 salinity results, errors, and parametric compensation

Because of time and equipment limitations during the salinity portion of the Lamina-2 calibration, we were not able to calibrate through a full range of salinity, and the limited salinity calibration range was not accomplished in a thermally stabilized tank. However, after overcoming problems associated with the taking of the salinity bottle samples and in establishing a reasonable dilution rate for changing the salinity of the test tank, we obtained encouraging, albeit preliminary, results. Future calibrations should include salinities over the full range from 0‰ to 40‰ and temperatures from 0° to 30°C.

In Fig. 4 we show the salinity change as measured by Lamina-2 in the calibration tank from 34‰ to 29‰ against time. The change in salinity was created by continuously diluting the seawater with distilled water while vigorously stirring the tank. Figure 4 shows how quickly the mixing occurs and the constancy in time of the resultant salinity. The change in the index of refraction in time as measured by Lamina-2 (not shown) is very similar in structure to that of salinity shown in Fig. 4; again, as in the salinity case, the index change occurs quickly and comes to a remarkably uniform level or “step” quickly. The temperature of the calibration tank increased by 1°C over the time of the calibration. This unfortunate lack of isothermal conditions was caused by the distilled water being 4°C warmer than the seawater with no temperature regulation of the calibration tank. This problem should be corrected in future calibrations.

A comparison of the salinity results as measured by the Lamina-2 salinity channel and by the salinometer (Guildline “Autosal” 8400) is shown in Fig. 8; three salinometer samples were taken at each of six stationary points, which are the horizontal “steps” shown in Fig. 4. The index of refraction difference as determined by subtracting the value measured by the Lamina-2 index channel from that calculated by SM (1990) using the OTM temperature and the Guildline salinity is shown in Fig. 9. Also, in Figs. 8 and 9 we have plotted a linear least squares fit to the errors; the fit is quite good with standard deviations of 0.0012 psu and 2.1 × 10⁻⁶ in the index, respectively. We note that the SM algorithm that was used to calculate the index of refraction from the salinity and temperature has a standard deviation of 5 × 10⁻⁶ in this regime, which is twice the standard deviation of the Lamina-2 data. We have excluded the last point at 28.976‰ psu, which we will discuss separately.

In spite of the algorithm uncertainties, there is clearly a systematic error in both the salinity and the index cases. The linear systematic character of these errors may be explained by an error (of 1.5%) in the linear coefficient between the fringe shift, δa, and δn in Eq. (1), or an error in the algorithms connecting δn, δT, and δS. It is possible that the SM algorithm used to calculate the index from T and S and the Vlasov/Lamina-2 algorithm used to calculate S from the index are independently in error. Figure 10 shows the salinity error with the linear component removed versus salinity; although this result is from a very limited calibration range in salinity, temperature, and time, it is very encouraging.

A plot of the salinity error against the index error is nearly linear with a nonzero slope (not shown); this suggests that, from Vlasov’s expression (1991) of δn_s = δn − (δn_T + δn_p), the salinity error is caused primarily by a basic index error of Lamina-2 as the salinity is changed. This will be investigated in future work.

Finally, the last point in Figs. 8 and 9 is understood in a different way. A look at 6300 and 6450 s on the x axis of Fig. 4 shows that something unusual happened at those times. The large discrepancy of this last point was caused by one whole fringe “dropping off” and being lost in the measuring photoelectronic scheme of Lamina-2. Such whole fringe “dropoff” is caused by the “threshold” of the software in the phasometer and does not affect the fractional fringe accuracy. We manually corrected this whole fringe dropoff by adding its salinity equivalent (0.149 psu) to data point 6, which now lies very near the rms linear regression from the previous five points. This gives the standarddeviation of 0.0023 psu for the limited range of our salinity calibration shown in Fig. 10.

In regards to the above unusual event that occurred at time t = 6300 s in Fig. 4, the rate of salinity and fringe change prior to this dropout was 0.15 psu min⁻¹ and 1.0 fringe per minute, respectively; this is an index of refraction change rate of the salt water of 26 × 10⁻⁶ min⁻¹. At the time of the fringe dropout, the rates had increased to 1.8 psu min⁻¹, 9.3 fringes per minute, and 320 × 10⁻⁶ min⁻¹. This fringe and index rate exceeded the fringe-counting cutoff of the software. As only one fringe was “hopped,” we will take this rate to be twice the local rate of change of the index and fringes that the present instrument configuration will accept. That is, the limits are 1 psu min⁻¹, 5 fringes per minute, and an index rate of 175 × 10⁻⁶ min⁻¹. This also suggests that our dilution techniques should be refined to minimize the difference between the bulk and the local rates of change. We note here that in the distilled water calibration case, the cooling produced a maximum index of refraction change of 5.5 × 10⁻⁶ min⁻¹. So, if we avoid this dropoff problem, the potential salinity accuracy is a few thousandths of a psu, which was a pleasant surprise from this preliminary work and will be more fully developed in future work. This result is shown more clearly in Fig. 10. We note here that if there had not been compensation for the effect of temperature on the optical path base length, the error in salinity would have been 0.03 psu.

As a final comment on the salinity errors, we should say something about the different salinity units used by Lamina-2 and by the salinometer. Lamina-2 uses ppt (parts per thousand), which is based upon chlorinity and titration; whereas, the salinometer uses psu, which is based upon conductivity ratios. From Lewis (1980) we know that for the same standard seawater sample these determinations can differ by up to 0.005 psu. If the samples are from coastal waters with a different ratio of salts than standard seawater, the difference can be up to 0.02 psu. As our seawater was from Vineyard Sound, these errors may be relevant to our work; however, because we set the salinities equal at the start of the run the magnitude of the error would be only up to 0.003 psu over the 6-psu change that was used. This is less than the noise of the salinity measurement by Lamina-2, which was ±0.005 psu. This noise figure can be seen in the thickness of the salinity curve during the horizontal “steps” (stationary points) of Fig. 4.