For radiometric calibration, the same care should be taken as when calibrating other spectrometer instruments to ensure that the calibration source input is spatially and angularly uniform across the slit.

Typically, the number of columns between the minimum and maximum wavelengths to be scanned is not divisible by the number of required wavelength groups. In this case, there are several methods:

1. Keep the column width constant and increment the pixel group width by a different amount than the column

2. Change column widths throughout the scan to allocate additional columns

3. Enforce constant column width and step size in certain wavelength regions.

The column width has changed in the second option, as shown below. Because the column width is varied, the amplitude measured at the detector will contain discontinuities.

These distribution methods can be used with line scan or multiplexed pattern sets. If there is overlap between patterns (some pixels are in multiple regions assigned to specific DMD pixel wavelength blocks), they first need to be separated into groups. Once the individual multiplexed scans have been completed, the results can be synthesized.

In a line scan mode set, energy of a specific wavelength is displayed on the DMD in only a single pattern. Therefore, there is a 1-to-1 correspondence between the mode number and the wavelength being measured. This can be represented mathematically, as shown below, a 3-mode sequence consisting of a 3×3 matrix, where each row contains the pattern displayed on the DMD, and each column contains the state of a specific band, on or off to represent a wavelength region of pixels.

In the case of this row scan, the identity matrix can define the scan regardless of the width of each individual pixel band.

In addition to line scan, there is also Hadama. As shown below.

4. Spectral decoding

Finally regarding,spectral decoding, since the AD sampling rate for most,applications is faster than the DMD mode rate, we have to,first calculate the average detector value for each mode scan,and then calculate the spectrum based on those average,detector values ​​for each pattern.

Sampling and Averaging During the scan, each pattern is displayed on the DMD for the required time period and samples are collected. There are two main ways to collect ADC samples.

1. Free running ADC

In this mode, the ADC is set up to continuously acquire samples. Incoming samples and trigger output status from the DLP controller indicating pattern exposure status.

2. Synchronous ADC

In this mode, the interrupt service routine is triggered to send a synchronization signal to the ADC.

Regardless of which mode is used, it may be necessary to discard some samples when the detector signal is not present, as shown in the figure below. The exact number and timing of using or discarding these samples will depend on the ADC's sampling rate and the detector's bandwidth, slew rate, and rise time. The last sample of the amplifier is usually discarded to prevent boundary effects on the data. The ready signal from the ADC occurs just before the pattern exposure ends. The remaining valid signals after removing any invalid samples are then averaged to reduce noise, resulting in a single detection value for each pattern.

In line scan mode, several steps must be performed to decode the spectrum:

1. Adjust detector stray light

In line scan mode, typically 99% or more of the DMD pixels are set to the off-state position for each pattern. We can average the detector values ​​over several black pattern periods and then subtract this DC value from all measurements. Detector stray light is periodic, not one-time.

2. Calculate the central wavelength of each pattern

For each pattern that needs to be calculated, the center column of the center row of the DMD, or more likely, is used for the calculation. This column number can then be used to calculate the center wavelength. and refer to another scan to calculate absorbance or any other required spectral calculations.

Hadamard scanning provides the ability to increase SNR over standard scanning in certain situations. A Hadamard code scan can be generated using two interleaved Hadamard codes. To calculate the spectrum, you need to do the following:

1. Compute the inverse of the S matrix used to define the set of Hadamard patterns.

2. Multiply the measured vector of each Hadamard scan (even and odd) by the inverse of the S matrix.

3. Truncate each resulting vector to the first N/2 entries, where N is the originally requested wavelength point or strip portion of DMD pixels.

4. Interleave the two vectors in the same order they were separated when creating the pattern.

For the case of N=8, the above process is shown in the figure below.

5. Coupling efficiency

The coupling efficiency, slit in a DLP spectrometer is higher than in an array detector spectrometer because the DMD is higher. Because of this, the coupling of light into the input slit should be designed to fill higher slits. With that in mind, here are some considerations for common lighting methods:

1. Transmittance

When using cuvettes or solid transmission samples that can be held in a collimated space, the lamp should be large enough to fill the height of the slit, but focused into the slit to maximize throughput into the spectrometer.

2. Diffuse reflection

The diffuse reflectance attachment should be designed to focus the illumination intensely on the high-brightness sample. The diffuse reflectance light should then be focused onto the slit, while the specular reflection should not be directed towards the slit. The illumination spot on the sample should be large enough so that when focused on the slit, the entire slit is filled.

3. Fiber coupling

If the system is designed for fiber coupling, the fiber bundle can be shaped to approximate the slit shape. On standard array-based systems, available slit heights are no higher than standard 600µm fiber. In DMD-based systems, this height may be in millimeters, depending on the DMD used and the magnification. Therefore, a larger percentage of light intensity can be allowed into the instrument from a standard circular fiber bundle that simulates a slit shape.

6. Scan parameters

1. Average number of scans: This is repeated back-to-back scans, averaged together. Averaging each wavelength point across multiple scans reduces noise while increasing the total scan time.

2. Wavelength range: The starting and ending wavelength of the scan (in nm) or the spectral range of interest.

3. Width (nm): This number selects the width of the pixel group in the generated column, or Hadamard pattern. The options shown correspond to the width of the dispersion spectrum in nm across the quantified pixel width.

4. Exposure time: AD sampling should be completed before the pattern exposure time ends.

5. Method: This controls the scanning method. Two options are provided: Column or Hadamard. Column scan selects one wavelength at a time. Hadamard scanning creates a wavelength that is multiplexed at once and then decodes each wavelength. Hadamard scan collects more light than column scan and provides greater SNR.

6. Resolution: Increasing the resolution will lead to oversampling of the spectrum. In general, set this resolution to oversample at least twice the desired full-width half maximum (FWHM). For example, for a resolution of 15 nm FWHM between 900 and 1700 nm, use the 2*(1700-900)/15≥107 wavelength point.