APPLICATION NOTE NO. 11Chelsea
Calculating Calibration Coefficients for Chelsea PAR Light Sensor with Built-In Log Amplifier
Revised February 2010

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This application note applies to the Chelsea PAR Light sensor, which has a built-in log amplifier.

This PAR sensor is compatible with the following Sea-Bird CTDs:

• SBE 9plus
• SBE 16 or 19 – This PAR sensor may not be compatible with 6-cell housing version of these CTDs; consult Sea-Bird.
• SBE 16plus, 16plus-IM, or 19plus  – CTD’s optional PAR connector not required when using one of these PAR sensors. The PAR sensor interfaces with an A/D voltage channel on the CTD.
• SBE 16plus V2, 16plus-IM V2, or 19plus V2 – The PAR sensor interfaces with an A/D voltage channel on the CTD.
• SBE 25 – CTD’s PAR connector (standard on current production SBE 25s, optional on older versions) not used with this PAR sensor. The PAR sensor interfaces with an A/D voltage channel on the CTD.

Note: The CTD voltage channel for use with the PAR sensor can be single-ended or differential.

SEASOFT computes PAR using the following:

PAR = [multiplier * 10⁹ * 10 ^{(V - B) / M} / Calibration constant] + offset

Enter the following coefficients in the CTD configuration (.con or .xmlcon) file:

M = 1.0 / (log ₁₀ e * A1 * 1000) = 1.0 / (0.43429448 * A1 * 1000)     (Note 2)

B = - M * log ₁₀ e * A0 = - A0 / (A1 * 1000)     (Note 2)

Calibration constant = 10 ⁹ / 0.046 = 2.174 x 10 ¹⁰

Multiplier = 1.0 for output units of μEinsteins/m^2.sec    (Note 3)

Offset =      (Note 4)

Notes:

1. In our SEASOFT V2 suite of programs, edit the CTD configuration (.con or .xmlcon) file using the Configure Inputs menu in Seasave V7 (real-time data acquisition software) or the Configure menu in SBE Data Processing (data processing software).
   Select Par/Irradiance, Biospherical /Licor as the auxiliary voltage sensor; the algorithm applies to the Chelsea PAR sensor as well.

2. A0 and A1 are constants from the Chelsea calibration sheet with an equation of form:
   PAR (in μWatts/cm²) = A0 + (A1 * mV)

3. The multiplier can be used to calculate irradiance in units other than μEinsteins/m^2.sec. See Application Note 11General for multiplier values for other units.
   The multiplier can also be used to scale the data, to compare the shape of data sets taken at disparate light levels. For example, a multiplier of 10 would make a 10 μEinsteins/m^2.sec light level plot as 100 μEinsteins/m^2.sec.

4. Offset: To determine the offset, enter M, B, Calibration constant, and Multiplier, and set Offset to 0.0 in the configuration (.con or .xmlcon) file. In Seasave V7, display the calculated PAR output with the sensor covered (dark); then enter the negative of this reading as the offset in the configuration (.con or .xmlcon) file.

1.   Chelsea computes:   PAR = K * e ^{(A0 + A1 * 1000 * V)}            (V = sensor output in volts)

2.   SEASOFT computes:   PAR = [multiplier * 10⁹ * 10 ^{(V - B) / M} / Calibration constant] + offset
(V = sensor output in volts)

3.   To determine Calibration constant, let multiplier = 1.0 and offset = 0, and set equations 1 and 2 equal to each other.

K * e ^{(A0 + A1 * 1000 * V)}  = 10 ⁹ * 10 ^{(V - B) / M} / Calibration constant

If e ^{(A0 + A1 * 1000 * V)}  = 10 ^{(V - B) / M} , then K = 10 ⁹ / Calibration constant     
→   Calibration constant = 10 ⁹ / K

where K = 0.046 for PAR units of μEinsteins/m^2.sec

4.   If e ^x = 10 ^y     →     log ₁₀ e ^x = y    and      x log ₁₀ e = y.

Let x = A0 + A 1 * 1000 * V        and        y = (V - B) / M

Let W = log ₁₀ e = 0.43429448    →   (A0 + A 1 * 1000 * V) W = (V - B) / M

→   W * A0 + W * A1 * 1000 * V = (V / M) – (B / M)    
→  (W * A0) + (W * A1 * 1000 * V) =   – (B / M) + (V / M)

Equating like terms:
(W * A1 * 1000 * V) = (V / M)     →     M = 1.0 / (W * A1 * 1000)
(W * A0) =  – (B / M)                    →     B =  - M * W * A0 = - A0 / (A1 * 1000)

Last modified: 05-May-2010

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