APPLICATION NOTE NO. 11QSP-PD
Calculating Calibration Coefficients for Biospherical Instruments PAR Light Sensor without Built-In Log Amplifier
Revised October 2012

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This application note applies to the following current output Biospherical Instruments PAR light sensors:

• QSP-200PD (no longer in production)
• QSP 2200 (PD) and QCP 2200 (PD) *

* Note: Biospherical’s 2200 series includes other instruments which are not compatible with Sea-Bird CTDs. Only the 2200 (PD) sensors can be integrated with Sea-Bird CTDs.

These PAR sensors are compatible with the following Sea-Bird CTDs:

• SBE  16, 16plus, 16plus-IM, 19, or 19plus CTD configured with an optional log amplifier and PAR sensor connector
  Note: Optional log amplifier and PAR sensor connector are not available on V2 SeaCATs (16plus V2, 16plus-IM V2, and 19plus V2)
• SBE 25 CTD configured with a log amplifier and PAR sensor connector (optional on older versions)
• SBE 9plus, 16, 16plus, 16plus-IM, 16plus V2, 16plus-IM V2, 19, 19plus, 19plus V2, 25, or 25plus CTD interfacing with a PN 90310 Log Amp Module. The Log Amp Module mounts on the CTD or cage, and connects to a single-ended or differential A/D voltage channel on the CTD.

The current output of these sensors is measured through a log amplifier in your CTD (or through the PN 90310 Log Amp Module) to obtain adequate resolution over the measurement range. Seasoft computes PAR using the following equation:

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

Enter the following coefficients in the CTD configuration file:

M = slope of log amplifier   (Note 2)

B = offset of log amplifier   (Note 2)

calibration constant C_S = 6.022 x 10 ¹³ / C_W   (Note 3)

multiplier = 1.0 for output units of microEinsteins/m² sec   (Note 4)

offset = 0, typically   (Note 5)

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).
2. Sea-Bird provides two calibration sheets for the PAR sensor in the CTD manual:

• Calibration sheet generated by Biospherical, which contains Biospherical’s calibration data.
• Calibration sheet generated by Sea-Bird, which incorporates the Biospherical data and generates M, B, and calibration constant C_S needed for entry in Sea-Bird software (saving the user from doing the math).

3. For calculation of C_W and C_S, see Mathematical Derivation below.
4. 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, for purposes of comparing 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.
5. Offset may be used to offset the data by a constant, if field data indicates a drift in the sensor. To calculate the offset:
   Enter M, B, calibration constant, and multiplier, and set offset = 0 in the configuration (.con or .xmlcon) file. With the sensor dark (covered), display the calculated PAR output in Seasave V7; then enter the negative of this reading as the offset in the configuration file.

C_W = Biospherical wet calibration factor from Biospherical calibration sheet [(quanta/cm^2.sec) / nAmp]

Output in water from Biospherical calibration sheet (quanta/cm^2.sec) = C_W * probe output (nAmp)

Output in water (quanta/cm^2.sec) = C_W * 10 ⁹ * probe output (Amp)

I = probe output (Amp)

Output in water (quanta/cm^2.sec) = C_W * 10 ⁹ * I

Output in water (quanta/m^2.sec) = C_W * 10 ⁹ * I * 10 ⁴ = C_W * 10 ¹³ * I

Output in water (μEinsteins/ m^2.sec) = C_W * 10 ¹³ * I / 6.022 x 10 ¹⁷
(see Application Note 11General for conversion from quanta to μEinsteins)

Seasoft calculates: Light (μEinsteins/ m^2.sec) = I x 10 ⁹ / C_S
where C_S = calibration constant

Equating the Biospherical and Seasoft relationships:

C_W * 10 ¹³ * I / 6.022 x 10 ¹⁷ = I x 10⁹ / C_S
C_W / 6.022 x 10 ¹³ = 1 / C_S
C_S = 6.022 x 10 ¹³ / C_W

Example:

C_W = Biospherical wet calibration factor from Biospherical calibration sheet = 4.77 x 10 ¹⁴ (quanta/cm^2.sec) / nAmp

Notes:

• See Application Note 11S for integrating a Surface PAR sensor with the SBE 11plus Deck Unit (used with the SBE 9plus CTD).
• See Application Note 47 for integrating a Surface PAR sensor with the SBE 33 or 36 Deck Unit (used with the SBE 16, 16plus, 16plus V2, 19, 19plus, 19plus V2, 25, or 25plus CTD).

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