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Spectrum 2D

The Spectrum 2D (two-dimensional) image modification function transforms image data (spatial domain) into the frequency domain and back via a 2D fast Fourier transform (FFT). By selectively passing or removing specific frequencies from the spectrum, filtered images may be reconstructed, yielding modified and enhanced versions of the image data.

The Spectrum 2D function may be used either as a high pass, low pass, or band pass, or notch filter. Practical applications include removing electrical and acoustic noise from images or isolating certain surface features (e.g., lathe lines on turned surfaces, load marks on ground or polished surfaces, etc.).

Using Spectrum 2D as a Low Pass Filter

Sometimes it is desirable to eliminate high frequency components of an image to better isolate and remove noise from an image. Typically, this would be done with the Spectrum 2D function by enclosing the central cluster of the spectrum within a passband. See Figure 1.

Figure 1: Passband Example

The objective here is to pass (allow) the central, longer wavelength portions of the plot, while stopping (disallowing) the shorter wavelength components located around the periphery of the plot.

When the image is reconstructed with its high frequency components removed, the most obvious change is smoother, more contiguous image features. Jagged lines and spikes are reduced, accentuating the longer wavelength features.

Using Spectrum 2D to Highlight Features (Band Pass Filter)

The Spectrum 2D function may be used to highlight certain surface features by filtering out spatial frequencies along a particular axis. It is possible to do this by drawing a band pass region over a particular region of the spectrum. This might be useful in isolating and accentuating smaller surface features inherent within lines oriented along a particular axis.

To filter out vertically oriented features, a passband should be drawn on with horizontal orientation on the spectrum. Horizontally distributed features would be passed, while vertically oriented features would be filtered. See Figure 2.

Figure 2: Horizontal Passband

Conversely, the vertically distributed features may be similarly examined by drawing a passband vertically, thus filtering out the horizontal components. See Figure 3.

Figure 3: Vertical Passband

Using Spectrum 2D to Remove Noise (Notch Filter)

If high frequency surface noise is evenly distributed across the spectrum, a passband around the center of the spectral plot could be used as low pass filter to remove multi-spectral high frequency features. However, if the image contains high frequency noise of a particular frequency, then Spectrum 2D may also be used as a Notch Filter to remove only the offending frequency.

If the noise source is a particular electrical or vibrational frequency, the frequency shows up in the FFT spectrum as spectral "hot spots". These spots may be removed by drawing a stop band over just these regions and then performing an InverseFFT. See Figure 4.

Figure 4: Example of Hot Spots

Depending upon the distribution and orientation of the noise bands, the hot spots should be distributed at the same angle in the spectral plot as they are on the image. There may also exist other spectral hot spots which are actually part of the surface features; however, these are usually distributed at some other orientation.

If the surface is anisotropic and includes some type of banding features naturally, isolating the noise bands proves more difficult, especially if they run parallel to the noise bands.

Spectrum 2D Procedure

Before beginning, it is advisable to make a backup copy of the original image file. The Spectrum 2D function is capable of making major changes to the image which, if saved, can destroy the original data.

The Spectrum 2D command allows filtering of images in the frequency domain through the 2-dimensional Fast Fourier transform (FFT). As the cursor is moved through the 2D plot, instantaneous results are displayed.

Rectangular boxes representing either frequencies to pass (multiply by 1.0), passband, or frequencies to stop (multiply by 0.0), stopband, can then be selected. Finally, the inverse transform is performed on the filtered transform data to reconstruct a new filtered image.

Use Spectrum 2D to correct the image distortion as follows:

 
  1. Select an image file from the Browse window at the right of the main window. Double-click the thumbnail image to select and open the image.
  2. You can open the Plane Fit view, shown in Figure 6, using one of the following methods: 
    • Right-click on the image name in the Workspace and select Add View > Spectrum 2D from the popup menu. See Figure 5.

Figure 5: Select Spectrum 2D from the Workspace

 

Or

  • Right-click on a thumbnail in the Multiple Channel window and select Spectrum 2D.

Or

  • Select Modify > Spectrum 2D from the menu bar.

Or
  1. Click the Spectrum 2D icon in the toolbar.

Figure 6: The Spectrum 2D View

 

A spectrum 2D (FFT) image of alkane, C60H122, is shown in Figure 6. The fundamental period is approximately 7.5 nm.

  1. Click the FFT button to perform a two dimensional Fast Fourier Transform on the data. The frequency spectrum image will appear in the image view.
  2. Sometimes the finer high frequency features of the transformed image are not visible without adjusting the color settings. Experiment with the color mapping using the Offset and Scale values (right click on the color scale) to best view the FFT spectrum's finer features. Refer to See "Color Scale" for details.
  3. Select regions to filter by right clicking to select the mode. Selected regions may either be marked to include in the filter with the passband Box or excluded with the Stop Band. See Figure 6,
  4. Due to the symmetry of the transformed data about the line fx = –fy, all Stopband and Passband boxes drawn actually produce two boxes on the display.
  5. If any Passband boxes exist on the display, then data outside the Passband boxes is deleted. Thus, it is superfluous to have a Stopband box completely outside the confines of a Passband box.
  6. Individual boxes and stopbands may be deleted by right clicking on an individual box and selecting the Delete command. The entire field of boxes and stopbands may be cleared with the Clear All command.
  7. When the desired regions are selected, click InverseFFT to return to the spatial domain.
  8. You may pass back and forth between the spatial and frequency domains, or you may Reload the image.
Parameter Description

Output File Name

Select the path of the modified image file.

Write File Upon Execute

Writes the output file when the FFT button is clicked.

Table 1: Input Parameters in the Spectrum 2D Panel

Parameter

Description

FFT

Initiates the two-dimensional FFT calculation.

Inverse FFT

Computes the modified image using the filter parameters defined in the FFT step.

Reload

Reloads the original image.

Table 2: Buttons in the Spectrum 2D Panel

 

Right-clicking an image in a Spectrum 2D, shown in Figure 6, window:
Parameter Description

Box

Puts the mouse in the passband mode. This allows placement of passband boxes which set the
frequency data outside the boxes to zero. Data inside the boxes is passed.

Stop Band

Puts the mouse in the stopband mode. This allows placement of stopband boxes which set the
frequency data within the boxes to zero. The data outside of the boxes is passed. Stopbands
appear on the top view image as “X-ed” rectangles.

Table 3: Controls in Spectrum 2D

 

Right-clicking inside a Box or Stop Band box in an (Fourier transformed) image, shown in Figure 6, window:
Parameter Description

Delete

Erases the passband Box or Stopband box that enclose the cursor.

Clear All

Deletes all passband Box and Stopband boxes.

Set Color

Allows you to set the cursor and/or box colors.

Table 4: Controls in Spectrum 2D (FFT)

Parameter Description

x Period

Spatial frequency in the x direction. The lowest frequency is at the center of the plot.

y Period

Spatial frequency in the y direction. The lowest frequency is at the center of the plot.

r Period

Spatial frequency in the radial direction.

Angle

Arctangent of (y/x).

Max Amp

The maximum amplitude (0-peak) of the transformed image.

Max RMS Amp

The maximum of the RMS amplitude of the transformed image.

Max Power

The maximum power of the transformed image.

Max Psd

The maximum power spectral density of the transformed image.

Amp

The amplitude of the 2D FFT at that spatial frequency.

RMS Amp

Amp/(sqrt(2))

Power

Amplitude2 = (2D FFT)2

Psd

Normalized power spectrum per number of points = (2DFFT * # x_points * # y_points)2/(# x_points * # y_points)

Rel Amp

Amplitude / (Max Amplitude)

Rel Psd

PSD / (Max PSD)

Table 5: Results Parameters in Spectrum 2D

 

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