Editing Magnetic circular dichroism (section)

== Measurement ==
The MCD signal ΔA is derived via the absorption of the LCP and RCP light as
:<math>\Delta A = \frac{A_- - A_+}{A_- + A_+}</math>

This signal is often presented as a function of wavelength λ, temperature T or magnetic field H.<ref name=gold/> MCD spectrometers can simultaneously measure absorbance and ΔA along the same light path.<ref>{{cite journal|author=G. A. Osborne|journal=Review of Scientific Instruments|date=1973|volume=44|pages=10–15|doi=10.1063/1.1685944|title=A Near-Infrared Circular Dichroism and Magnetic Circular Dichroism Instrument|issue=1|bibcode = 1973RScI...44...10O }}</ref> This eliminates error introduced through multiple measurements or different instruments that previously occurred before this advent.
The MCD spectrometer example shown below begins with a [[monochromator|light source that emits a monochromatic wave of light]]. This wave is passed through a [[Rochon prism]] [[linear polarizer]], which separates the incident wave into two beams that are linearly polarized by 90 degrees. The two beams follow different paths- one beam (the extraordinary beam) traveling directly to a [[photomultiplier]] (PMT), and the other beam (the ordinary beam) passing through a [[photoelastic modulator]] (PEM) oriented at 45 degrees to the direction of the ordinary ray polarization. The PMT for the extraordinary beam detects the light intensity of the input beam. The PEM is adjusted to cause an alternating plus and minus 1/4 wavelength shift of one of the two orthogonal components of the ordinary beam. This modulation converts the linearly polarized light into [[circularly polarized]] light at the peaks of the modulation cycle. Linearly polarized light can be decomposed into two circular components with intensity represented as <math>I_0 = \frac 12(I_- + I_+)</math>

The PEM will delay one component of linearly polarized light with a time dependence that advances the other component by 1/4&nbsp;λ (hence, quarter-wave shift). The departing circularly polarized light oscillates between RCP and LCP in a sinusoidal time-dependence as depicted below:

[[File:The description of the circular light.png]]

The light finally travels through a magnet containing the sample, and the transmittance is recorded by another PMT. The schematic is given below:

[[File:The mechanism of the instrument.png]]

The intensity of light from the ordinary wave that reaches the PMT is governed by the equation:

<math>I_\Delta=\frac {I_0}2\left[\left(1-\sin\left(\delta_0\sin \omega t\right)\right)10^{-A_-}+\left(1+\sin\left(\delta_0\sin\omega t\right)\right)10^{-A_+}\right]</math>

Here A<sub>–</sub> and A<sub>+</sub> are the absorbances of LCP or RCP, respectively; ω is the modulator frequency – usually a high acoustic frequency such as 50&nbsp;kHz; ''t'' is time; and δ<sub>0</sub> is the time-dependent wavelength shift.

This intensity of light passing through the sample is converted into a two-component voltage via a current/voltage amplifier. A DC voltage will emerge corresponding to the intensity of light passed through the sample. If there is a ΔA, then a small AC voltage will be present that corresponds to the modulation frequency, ω. This voltage is detected by the lock in amplifier, which receives its reference frequency, ω, directly from the PEM. From such voltage, ΔA and A can be derived using the following relations:

<math>\Delta A= \frac{V_{ac}}{1.1515V_{dc}\delta_0\sin\omega t} </math>

<math>A=-\log( \frac{V_{dc}}{V_{ex}} )</math>

where V<sub>ex</sub> is the (DC) voltage measured by the PMT from the extraordinary wave, and V<sub>dc</sub> is the DC component of the voltage measured by the PMT for the ordinary wave (measurement path not shown in the diagram).

Some [[superconducting magnet]]s have a small sample chamber, far too small to contain the entire optical system. Instead, the magnet sample chamber has windows on two opposite sides. Light from the source enters one side, interacts with the sample (usually also temperature controlled) in the magnetic field, and exits through the opposite window to the detector. Optical relay systems that allow the source and detector each to be about a meter from the sample are typically employed. This arrangement avoids many of the difficulties that would be encountered if the optical apparatus had to operate in the high magnetic field, and also allows for a much less expensive magnet.