Select an article below to understand the options for processing acquired FTIR data.

You can perform basic equations (add, subtract, multiply and divide) with acquired sample spectra. There are a number of reasons why you might want to do this, especially for subtracting a reference spectrum. For more information, see the sections that follow.

## To perform any spectral math operation

To perform spectral math, the sample and reference spectra must have the same spectral resolution and be in the same Y-axis unit. If they are not, the software automatically converts the selected reference spectrum to match the selected sample spectrum. In order to subtract, multiply or divide spectra, at least a portion of the spectral range (X-axis) of the two spectra must overlap.

### To perform any spectral math operation on a spectrum

- Acquire or open a spectrum of your sample and make sure that spectrum is selected in the spectral view.
- Choose
**Process**(menu) >**Spectral Math**.

The software opens the Spectral Math setup window with the sample spectrum in the left pane and space for a reference spectrum in the right pane.

**Figure 1.**Spectral Math Setup Window - Spectrum of selected sample
- Selected reference opens here
- Selected math operation

- Use the settings list between the two panes to select a spectral math operation (Subtract, Add, Multiply or Divide).
- Use the Select Reference list to search for a spectrum in the current project, another project, or from a spectral library.
- Click
**Subtract**(Add, Multiply, Divide) to start the operation.

The software opens the Spectral Math operation window with the two original spectra (bottom) and the current result with a factor slide bar (top). Here is an example showing a subtraction result: - Current subtraction result
- Factor
- Sample
- Reference

- Adjust or enter a factor as needed to increase or decrease the intensity of the reference in the result spectrum.

See the sections below for tips on adjusting the factor for each math type. - Choose
**Save**.

The software shows the spectral view with the subtraction result in the spectral pane and at the top of the results panel, with the original sample and reference spectra directly below it. - Spectral math result
- Sample
- Reference

**Note** Use the bottom bar to change the Factor’s adjustable range.

## Subtract one spectrum from another (A-B)

Use Subtract to subtract one spectrum from another. Spectral subtraction is useful in a variety of situations. Here are some examples:

- If you measure a sample that is dissolved in a solvent, the spectrum will contain peaks due to the solvent. By subtracting a spectrum of the pure solvent from the sample spectrum, you can eliminate the solvent peaks and produce a “clean” spectrum of the sample material.
- When you measure a sample that is a mixture of two or more components, the spectrum is, theoretically, the sum of the spectra of all the components. By subtracting a spectrum of a pure component from the sample spectrum, you can produce a simpler mixture spectrum with that component removed. You can then search that spectrum against a library to identify the remaining components. (In this case, you might want to try using the Multi-Component Search option instead.)
- If you measure a sample that contains an unknown contaminant, the spectrum will contain peaks due to the contaminant. By subtracting a spectrum of uncontaminated sample material from the first spectrum, you can produce a residual spectrum of the contaminant. You can then search that spectrum against a library to identify the contaminant.
- If you collect spectra to monitor the quality of a material being produced, you can more easily detect changes from one batch to the next by subtracting one sample spectrum from the next (or vice versa) than by just comparing the spectra visually.

### Tips on subtracting spectra

- To determine the subtraction factor, watch the changes in the common peaks as you change the factor. The common peaks in the result spectrum should become smaller. The optimum factor is one which produces nulled (or zeroed) common peaks in the subtraction result without subtracting other important spectral information. If you use the correct factor, the peaks present in the result will be due solely to the sample material of interest.
- The initial subtraction factor is automatically calculated from the displayed region. If you display a different spectral region and perform the subtraction again, the difference spectrum will probably be different because the subtraction factor changed.
- When you subtract a reference spectrum from a sample spectrum, the baseline regions are subtracted along with the regions that contain peaks. If the sample spectrum's baseline is not flat and at zero absorbance (or 100% transmittance), the baseline of the subtraction result will have the same undesirable characteristics. If you correct the baseline first, you can obtain a “clean” subtraction in which corresponding peaks are subtracted out, without baseline problems in the result.
- When you subtract the spectrum of a pure reference material from that of a mixture, the peaks may not subtract cleanly. This is because the reference spectrum does not account for any changes that may occur due to molecular interactions with the other components in the mixture or differences in relative concentrations of components. These conditions may cause some peaks to shift slightly or change shape.

## Add two spectra together (A+B)

Use Add to add two spectra together. Adding spectra can be useful in the following situations:

- Add can be used to join together two spectra of different spectral ranges.
- By adding two pure component spectra together, you can produce a theoretical composite spectrum that is the sum of the two component spectra. This theoretical composite spectrum can be compared with an unknown mixture spectrum in a quantitative analysis.

### Tips on adding spectra

- Use the Factor setting to scale the reference spectrum up or down before adding it to the sample spectrum.
- If only one of the spectra contains data points in a spectral region, the Y value of the other spectrum is considered to be zero in that region when the spectra are added.

## Multiply one spectrum by another (A*B)

Use Multiply to multiply two spectra. Most people use divide rather than multiply for most applications. But multiplying spectra can be useful for reprocessing a spectrum with a different background. For example, if you measure a sample that is adhered to a matrix, you can acquire a single beam spectrum of just the matrix and use that spectrum to cancel out the original background and replace it with the new one. Here is the equation:

S * B_{1}/B_{2}

Where:

S= sample spectrum (processed with original background)

B_{1} = original background

B_{2} = new background

## Divide one spectrum by another (A/B)

Use Divide to divide one spectrum by another. Dividing spectra can be useful for reprocessing a spectrum with a different background. For example, if you measure a sample that is adhered to a matrix, you can acquire a single beam spectrum of just the matrix and use that spectrum to cancel out the original background and replace it with the new one. Here is the equation:

S / (B_{2}/B_{1})

Where:

S= sample spectrum (processed with original background)

B_{1} = original background

B_{2} = new background

### Tips on dividing spectra

- Data points that have zero absorbance values in the original sample spectrum will produce very strong absorbance values in the resulting spectrum.

## Using spectral math with data security

When “Require reason for change for Spectral Math” is enabled in the Thermo Scientific Security Suite, Spectral Math requires a change reason and signature before the results can be saved, and the following change event is recorded in the audit log:

- Date and time
- Operation performed: subtract, add, multiply, divide
- Sample spectrum title
- Reference spectrum title
- Factor

Advanced Spectral Math provides more flexibility and power than standard spectral math. While standard spectral math supports spectral subtraction, addition, multiplication, and division using a single reference spectrum, Advanced Spectral Math allows you to build custom equations using up to 10 reference spectra and using a wider range of operations.

For many applications, using the standard subtract, add, multiply, and divide functions in spectral math is simple and sufficient. However, if your analysis requires a more complex equation, Advanced Spectral Math may be required.

Both forms of spectral math are available only in the Desktop interface of OMNIC Paradigm software.

When choosing between the two methods, consider the following differences to decide which tool is right for you:

- Standard Spectral Math
- Supports only subtraction, addition, multiplication, and division using a single reference spectrum with a slider to adjust the factor

- Advanced Spectral Math
- Flexible equation builder using basic subtraction, addition, multiple, and division as well as derivatives, exponents, and more
- Can include up to ten different reference spectra in the equation

### Carrying out advanced spectral math

When you use Advanced Spectral Math, you will typically add spectra that you will use in the equation, build your equation, preview the results, and finally review the result in the Spectral View.

#### To perform advanced spectral math

- In the Spectral View, select a measurement to use in Advanced Spectral Math.
- Open the
**Process**menu and select**Advanced Spectral Math**. The equation builder opens.

- Add reference spectra to use in the equation.

You can add up to 10 spectra, and you do not need to use every spectrum that you open. You may find that it is easier to add the spectra first so that they are available while you focus on the equation, or you may prefer to add them only as needed.

- Select reference or library spectra. When you add a spectrum, a new tab opens automatically.

- If you use a spectrum from a commercial (locked) library in the equation, you cannot export the result.

- Build the equation.

- Click an operator to add it to the equation.
- Once the operator is added, you can click any of the open "?" spaces to insert a spectrum or another operator.

- To add a spectrum, with the open space selected, choose a spectrum and click Insert into Equation.
- To add an operator, click the operator. If you have an open "?" space selected, the operator is inserted into that location. If you do not have any spaces selected, the new operator is wrapped around the the current equation.
- You can also save your equation or load a previous equation.
- To save the equation, simply click Save. The equation is added the list of available equations.
- To load a previous equation, you must first open the correct number of spectra used in the equation. For example, if the equation used 3 spectra (A, B, and C), open at least 3 spectra. Your open spectra will automatically be inserted into the equation in their corresponding position, but you can edit the equation as needed or replace the spectra.

- When you are satisfied with the equation, click
**Calculate**to preview the result.

- Preview the result.

- To edit the equation, click Cancel to return to the previous screen.
- To save the results of the equation, enter a name for the resulting spectrum or leave the default and click Save.

- View the result in the Spectral View.

The resulting spectrum is listed in the Results pane. Spectra used in the equation are shown in the sub-panes below the result spectrum with a label indicating their use in the equation.

### Functions available in advanced spectral math

Functions | Description |
---|---|

k | Constant |

? + ? | Addition |

? - ? | Subtraction |

? * ? | Multiplication |

? / ? | Division |

log(?) | Logarithm. Returns the base 10 log |

exp(?) | Returns the result of the constant e (2.7182818) raised to the power of the specified value |

sqrt(?) | Square root of the value |

deriv(?) | Derivative |

savderiv(?) | Savitsky-Golay derivative |

norderiv(?) | Norris derivative |