Light transfer and reported light intensities

The aquatic chamber has an attachment for placing LI-COR LI-190R Quantum Sensor on the viewing window, to measure how much light is getting through the sample. The measurement can be used to estimate the absorbed quanta relative to a clear water sample, as shown in the following deviation.

Q_f is the flux of photons (µmol m^-2 s^-1) from the fluorometer incident on the window of the sample cell (Figure 10‑19), and Q_exit is the flux leaving the opposite window. The windows (when clean) each have a transmittance g of 0.981 Measurements done at LI-COR using an integrating sphere..

What are the "knowns"? On the fluorometer side, we know Q_f , what the fluorometer is generating. If window transmittance τ_g is specified, then we actually have Q_in reported directly, since the fluorometer takes transmittance into account when setting light levels.

There is a subtlety here: The fluorometer is calibrated with a 6 cm² aperture, but when used with the aquatic chamber, the aperture is 7.92 cm². If the fluorometer's light output were perfectly uniform, then increased area would not change the irradiance, since it is on a per area basis. However, the light output is brightest near the edges, and the area increase results in about 20% more light output than expected. This is accounted for in the transmittance factor of 1.18 that is applied when using the aquatic chamber, which includes the window transmittance of 0.98. For example, if you set the fluorometer to 1000 µmol m^-2 s^-1, it will actually set itself to 1000 / 1.18 = 847 (according to its 6 cm^-2 based calibration), The actual output is some 20% higher (1020), which reduces to the 1000 you asked for when it passes through the window into the aquatic chamber.

Outside the opposite window is a quantum sensor reading q, from which we can estimate Q_exit. To do this, we must account for calibration differences (due to light spectra, field of view, etc.) between the fluorometer and the particular sensor being used. This difference depends on color (red and blue fractions f_r and f_b), so we use an empirically determined adjustment factor for each, a_r and a_b. These are measured using a dry, empty aquatic chamber with a procedure described below. It is assumed we know the effective transmittance of light through a dry, empty chamber. This has been measured using a fluorometer and an integrating sphere to collect the light. For red, the value is 0.54, and for blue, it is 0.51.

Once a_r and a_b are known, we can now get Q_exit and Q_out from q:

10‑72

10‑73

The cell transmittance (τ) is computed from

10‑74

If the sample cell were a perfect "light pipe", the transmittance would be 1.0 when the cell is empty. In reality, it is closer to 0.5, because of light losses to interior surfaces; filling the sample cell with clear water actually increases the transmittance slightly. Since what is of interest is how many photons are being absorbed in the algal sample, we can use an empirically determined clear-water transmittance (τ_w), as a reference, and compute a transmittance (and absorptance) relative to that.

With clean water in the sample cell, we use equation 10‑74 to get an expression for clean water transmittance τ_w:

10‑75

Since red and blue are scattered slightly differently in the cell, the determination of w should actually be done twice: once for red light (f_r = 1) yielding w_r, and once for blue f_b = 1, yielding w_b. Typical values are w_r = 0.58 and w_b = 0.57. Then, for any mix of f_r and f_b, the appropriate color-weighted water transmittance (w) is

10‑76

With an algal sample in place, we again use equation 10‑74 to write the expression for transmittance τ_s through that sample:

10‑77

Given these two transmittances, we can compute2 Thanks to Marcel Janssen, AlgaePARC, Wageningen University & Research for this analysis. the average light intensity within the sample cell, and the portion of it that is absorbed by the algae. To do this we assume light extinction in the sample cell is a Beer's law process. For water

10‑78

and for water plus algae

10‑79

where ϵ_w and ϵ_s are extinction coefficients, and d is the optical depth (arbitrary, because it cancels out in the final equations).

The extinction coefficient for algae by itself is then

10‑80

The average light intensity (Q_avg) in the sample cell is

10‑81

The light absorbed by just the algae (Q_abs) within the sample cell is

10‑82

The rate (in mol s^-1) at which photons are being absorbed by the algae is.

10‑83

where S_w = 7.92× 10^-4, the area (m²) of the aquatic chamber's window that faces the fluorometer.

Figure 10‑20 illustrates how Q_avg and Q_abs change with Q_out for a fixed Q_in.

We have neglected the effect of the pump and resulting bubbles in the analysis up to now, but bubbles have a significant effect, typically reducing measured Q values (and thus computed sample and water values) by a factor of 0.7 to 0.8. To handle this effect, we introduce one more empirical constant B, which is simply

10‑84

where Q|_on is the external quantum sensor reading with the circulation pump on, and Q|_off when it is off.

We apply B when computing the effective clear water transmittance, which is now corrected for color and bubble effect:

10‑85

Implementation details

The aquatic light measurements and computations described above are contained in the AquaticQ group, and can be viewed in the Measurements screen (Figure 10‑21).

The sources of the parameters used in the above computations are shown in Table 10‑2. The five empirical constants (a_r; a_b; w_r; w_b; B) are accessible on Constants > Aquatic Chamber, but more typically are set using the calibration screen (see Setting the light calibrations). In the fluorescence computations (group = Flr), the computations are the same, but some labels and units change. With the aquatic chamber, the "non-basis" Flux value from GasEx is used for "assimilation", and the quantum flow value Q^*_abs is used for "absorbed" light. This allows a computation of PhiCO2, and changes the units of ETR as shown in the table.

Table 10‑2. Measurements, constants, and computations pertaining to light absorption for the aquatic chamber.

Group	Label	Description
AquaticQ	Qin	Qin - Flux incident on sample, reported by fluorometer (µmol m-2 s-1).
	Qout	Qout - Estimated quantum flux leaving the sample (µmol m-2 s-1).
	Qavg	Qavg - Average quantum flux within the sample.
	Qabs	Qabs - Absorbed quantum flux by sample (µmol m-2 s-1).
	Qabs*	Q*abs - Absorbed flow of quanta by sample (µmol s-1).
	tau_w	τw - Transmittance for clear water, corrected for color and bubble effect.
	tau_s	τs - Transmittance of sample (µmol s-1).
Aquatic	Red adjust	ar - PAR sensor cal adjust factor for red.
	Blue adjust	ab - PAR sensor cal adjust factor for blue.
	tau_wr	τwr - Clear water transmittance for red light.
	tau_wb	τwb - Clear water transmittance for blue light.
	bubble	B - Reduction in transmission due to bubbling.
FlrLS	Q	Qin - Flux incident on sample (µmol m-2 s-1).
	f_red	fr - fraction red
	f_blue	fb - fraction blue
Meas	Qamb_out	q - External PAR sensor reading (µmol m-2 s-1).
Flr	Qabs*_fs	From AquaticQ:Qabs*, at time of light adapted flash (µmol s-1).
	Flux*_d	From GasEx:Flux at time of dark adapted flash (µmol s-1).
	Flux*_fs	From GasEx:Flux at time of light adapted flash (µmol s-1).
	ETR	Now has units of (µmol s-1). ETR = Φps2fps2fq

Setting the light calibrations

A calibration page is provided for determining the five constants required to compute absorbed light in the aquatic chamber (Figure 10‑22). All of these procedures require the external quantum sensor to be mounted on the viewing window of the aquatic chamber.

The chamber state determines which factors can be measured. The first, Dry and Clean, is used to measure the adjustment factors for a particular quantum sensor. This need be done only once for a particular sensor.

With the chamber filled with clean fresh media, the red and blue chamber water transmittances can be measured (Figure 10‑23). The transmittance of a wet chamber depends strongly on the volume of liquid in the chamber. When measuring w_r and w_b, be sure to use the same volume as you intend to use with algal samples.

With the chamber filled with an algal sample, the only calibration that can be done is for the bubble effect (Figure 10‑24).