6. Signal Processor

As shown in Figure 14, the CPL spectrometer captures both the AC (ΔI) and DC (I_A) components of the signal. These values are used to calculate the degree of ellipticity (θ), which is the vertical axis when plotting CPL data. This allows CPL to be represented based on the same definition as the ellipticity commonly used in CD measurements.

Let E_L and E_R represent the electric field amplitudes for LCP and RCP light, respectively. Assuming that the luminescence is propagating directly towards the detector and E_L > E_R, the combined electric field vectors form an elliptical polarization pattern (Figure 15). The minor axis amplitude (x-direction) is E_R – E_L , and the major axis amplitude (y-direction) is E_R + E_L. The ellipticity angle θ is defined as the angle between the major and minor axis vectors relative to the origin.

Fig. 15  Relationship between electric field vector and degree of ellipticity for LCP and RCP light

The relationship between E_L, E_R and θ is expressed by:

Since the relationship between the light intensity I and the amplitude E of the electric field vector is expressed as

Equation (2) can be rewritten as:

Multiplying both sides of Equation (4) by (√(I_L)+√(I_R)) finally yields:

Since the difference between I_L and I_R is negligibly small, it can be assumed that I_L≈I_R≈I_A. Therefore,

is obtained. Next, the units for the degree of ellipticity are converted from radians to millidegrees. Since θ_rad is very small, the following equation holds:

By substituting Equation (7) into Equation (6), the following equation is obtained:

In actual CPL measurements, the raw data obtained are θ_mdeg or θ_mdeg‘, together with DC, which are related by the following equation.

For the CPL-300, a (1S)-(+)-10-ammonium camphorsulfonate aqueous solution is used to calibrate the vertical axis (θ_mdeg). The CD value at 290.5 nm for a 0.06% (w/v) aqueous solution of this substance is known to be +190.4 millidegrees for an optical path length of 10 mm, and this is used as the scale standard for CD spectrometers. This solution is placed in the sample compartment, and both the excitation and emission wavelengths are set to 290.5 nm. Since the difference between the transmitted LCP and RCP light intensity due to the circular dichroism exhibited by the sample is accurately known, this is used to calibrate the instrument, as described in detail below. The CD value for the (1S)-(+)-10-ammonium camphorsulfonate aqueous solution is +190.4 millidegrees, indicating that absorption of LCP light is larger than that of RCP light, so that the transmitted RCP light intensity is higher than the transmitted LCP light intensity. Assuming that the circularly polarized component of the transmitted light can be regarded as CPL, the fluorescence intensity is higher for RCP light as in the case of transmitted light. Therefore, when the (1S)-(+)-10-ammonium camphorsulfonate aqueous solution is measured using CPL spectroscopy, the signal is negative and the intensity is −190.4 millidegrees.

When converting the vertical axis units from θ_mdeg‘ to ΔI, the following equation, which is based on Equations (8) and (9), is used:

The vertical axis units are converted from θ_mdeg‘ to ΔI using: