Common Spectral Measurement Modes and Calculation Principles

Common Spectral Measurement Modes and Calculation Principles

Overview

In the daily use of fiber spectrometers, the two most common measurement modes are transmission measurement and reflection measurement. The core mathematical principle of the two modes is exactly the same — both convert the detector's raw counts into physically meaningful transmittance / reflectance and absorbance through dark background subtraction and reference normalization. This article details the formula derivation, optical-path setup and standard operating steps for the two optical-path modes.

1. Core Formula Derivation

Whether in transmission or reflection optical paths, the calculations are based on the same set of formulas; the only difference is the substitution of the physical quantity names.

1.1 Transmittance / Reflectance Formula

$$T = \frac{Sample - Dark}{Reference - Dark} \quad \text{or} \quad R = \frac{Sample - Dark}{Reference - Dark}$$

where:

1.2 Absorbance Formula

Taking the logarithm of the transmittance / reflectance formula yields the absorbance:

$$A = \lg\frac{1}{T} = -\lg T = \lg\frac{Reference - Dark}{Sample - Dark}$$

As can be seen from the formula, to obtain an accurate absorbance value, three sets of data — Dark → Reference → Sample — must be measured in sequence, and all three must be acquired under the same integration time and number of averages.

Core principle: The dark background and reference should be re-acquired at the beginning of each measurement sequence to eliminate the effects of light-source drift and ambient temperature variation. Keep all parameters (integration time, number of averages) consistent throughout the measurement.

2. Transmission Optical Path

2.1 Definition and Applicable Scenarios

The transmission optical path is one in which the incident light passes through the sample before being received by the spectrometer, and is used to measure the sample's absorption of the incident light.

Common application scenarios:
- Liquid samples: solutions in cuvettes or flow cells
- Solid transmission: flat transparent/semi-transparent solids such as filters, films and glass

2.2 Liquid Transmission (Cuvette Holder)

Optical path diagram: Light source → cuvette (containing the sample liquid) → optical fiber → spectrometer

Operating steps:

1. Turn on the light source, place an empty cuvette (or a cuvette containing the reference liquid), and adjust the integration time so that the maximum spectral intensity falls within 50,000-55,000 counts
2. Turn off the light source and click [Dark Background] to store the Dark
3. Turn on the light source and click [White Reference] to store the Reference
4. Switch to transmittance mode; the transmittance displayed within the effective wavelength range should now read 100%
5. Place the cuvette containing the sample liquid and observe the transmittance distribution curve in real time in transmittance mode
6. Click [Save] to store the current transmittance value
7. Switch to absorbance mode to observe the absorbance curve, then click [Save] to store it

2.3 Liquid Transmission (Immersion Probe)

When it is inconvenient to sample into a cuvette (e.g. online process monitoring), an immersion probe can be inserted directly into the solution.

Operating steps:

1. Turn on the light source, immerse the probe in the reference liquid (e.g. pure water), and adjust the integration time to 50,000-55,000 counts
2. Turn off the light source → [Dark Background]
3. Turn on the light source → [White Reference]
4. Switch to transmittance mode and confirm 100% is displayed
5. Immerse the probe in the sample liquid, observe and save the transmittance and absorbance curves

2.4 Solid Transmission

Suitable for solid samples that do not require a cuvette, such as thin films and filters.

Operating steps:

1. Turn on the light source and adjust the integration time to 50,000-55,000 counts
2. Turn off the light source → [Dark Background]
3. Turn on the light source → [White Reference] (air serves as the reference)
4. Switch to transmittance mode and confirm 100%
5. Place the solid sample in the optical path, observe and save the data

3. Reflection Optical Path

3.1 Definition and Applicable Scenarios

The reflection optical path is one in which the incident light strikes the sample surface and the reflected light is received by the spectrometer, and is used to measure the sample surface's reflection of the incident light.

Common application scenarios:
- Regular solids: ceramics, metals, plastic sheets
- Powder samples: powders after compaction
- Opaque materials such as coatings and textiles

3.2 Reflectance Probe Optical Path

Optical path diagram: Light source → Y-type reflectance probe (emission fiber → sample → receiving fiber) → spectrometer

Operating steps:

1. Turn on the light source, aim the probe at a standard white tile (Spectralon or BaSO₄), and adjust the integration time to 50,000-55,000 counts
2. Turn off the light source → [Dark Background]
3. Turn on the light source → [White Reference]
4. Switch to reflectance mode and confirm 100% is displayed
5. Aim the probe at the sample to be measured, observe and save the reflectance and absorbance curves

3.3 Relationship Between Reflectance and Absorbance

In reflection measurements, absorbance is commonly used for near-infrared quantitative analysis (e.g. grain moisture and protein detection):

$$A_R = \lg\frac{1}{R} = \lg\frac{Reference - Dark}{Sample - Dark}$$

Combined with chemometric methods, reflectance spectra enable the simultaneous and rapid prediction of multiple components in solid samples.

4. Key Precautions

This article was compiled by Pynect.