Figure 2 shows a schematic of the static characterization, whereby a spectrometer (F-7000, Hitachi High-Tech Corporation, Tokyo, Japan) was used to capture the spectral emission from the PC-PSP test plate under steady conditions. A test chamber was connected to both a pressure controller and a temperature controller. The pressure controller achieved the target pressure with 10 Pa accuracy, and the temperature controller had accuracy on the order of the second decimal degree. By controlling the pressure and temperature in the test chamber, pressure and temperature calibrations were obtained for the steady-state quantities of interest: luminescent intensity change, and pressure sensitivity. The excitation wavelength was 465 nm, and the excitation area covered the whole surface of the test plate. The spectrometer acquired the emission spectrum from 560 to 700 nm, including the 0.125% noise. The reference pressure and temperature were 100 kPa and 303 K, respectively. Dry air was pumped into the test chamber to minimize the effect of humidity on the PC-PSP [

16]. The configuration of the optical setup was consistent across all measurements.

Theoretically, the luminescent intensity,

I, is the product of the gain of the photo-detector in the spectrometer,

G; the emission spectrum from the PC-PSP test plate,

I_{PCPSP}; the excitation intensity in the spectrometer,

I_{ex}; and a factor of due to the measurement setup,

f_{set}, as described in Equation (1) [

17]:

Due to consistency in the measurement setup,

G, I_{ex}, and

f_{set} were constant for all tests so that

I_{PCPSP} was the only variable in the static characterization. During the pressure calibration, pressure,

P, in the test chamber was varied from 5 to 120 kPa at the controllable reference temperature,

T_{ref}. The luminescent intensity ratio of the PC-PSP,

I(P_{ref},T_{ref})/I(P,T_{ref}) is described by the Stern–Volmer relationship in Equation (2) [

1]:

where the subscript,

ref, represents the reference conditions.

A and

B are calibration constants, which are functions of temperature. Because of the adsorption of oxygen molecules onto the porous layer, the intensity ratio of the PC-PSP behaves nonlinearly with changes in pressure [

18]. Instead of a linear relationship, a second-order polynomial relationship is applied, as follows:

where

A_{P},

B_{P}, and

C_{P} are calibration constants for the second-order polynomial fit. During actual unsteady pressure measurements, however, there can be a substantial difference in the reference temperature and the temperature during pressure measurements. In such an uncontrolled case, the measurement temperature,

T, in the test chamber is different from the reference temperature,

T_{ref,unc}. In this case, the equation for the reference intensity,

I(P_{ref},T_{ref,unc}) is different from the luminescent intensity,

I(P_{ref},T_{ref}), described in Equation (4) due to the temperature difference between the reference and measurement temperatures:

where,

A_{P,unc},

B_{P,unc}, and

C_{P,unc} are calibration constants under the uncontrolled reference temperature,

T_{ref,unc}. From Equation (3), the pressure sensitivity,

σ, is defined as a slope of the luminescent intensity ratio:

Due to thermal quenching, the luminescent intensity of the PC-PSP,

I, is dependent on the temperature. The normalized luminescent intensity,

I(T)/I(T_{ref}), can be described with empirically-based polynomial functions. The first-order polynomial fit is

where,

A and

B are calibration constants under the first-order polynomial fit. The measurement temperature,

T, in the test chamber was controlled from 273 to 333 K in 10 K steps to obtain the functional relationship between the normalized luminescent intensity and the temperature ratio during calibration. The reference pressure in the chamber was maintained at 100 kPa. A second-order polynomial fit can also be used to increase the number of terms to fit the calibration data [

11,

19]:

where,

A_{T},

B_{T}, and

C_{T} are calibration constants for the second-order polynomial fit. If the measurement temperature,

T, is the same as the reference temperature,

T_{ref}, the normalized luminescent intensity ratio is unity.

In the same manner as with pressure sensitivity, the luminescent intensity change,

δ, for the first-order polynomial fit was defined as the slope of the normalized intensity,

I(T)/I(T_{ref}), at the reference temperature.