Tool Window - Fourier Transform

You can have the Fourier transform of an image computed for you. The Explorer group in the Fourier Transform tool window gives you an overview of which FT images are currently loaded in your software and to which images they belong.

Should this tool window not be visible, use the View > Tool Windows > Fourier Transform command to show the tool window.

Structure of the tool window

The tool window is made up of several parts. Click on one of the areas in the tool window shown above to jump to the corresponding help topic.

(1) The tool window's toolbar

In the Fourier Transform tool window's toolbar the following buttons are at your disposal. The buttons are described in the following table.

	FT on Full Image	Click this button to compute a Fourier transform from the full active image and to have it displayed in the image window.
	FT on ROI	Click this button to compute a Fourier transform from a self-defined square or rectangular image segment.
	Inverse FT	Click this button to carry out an inverse Fourier transform.
	Remove Link	When you compute an FT image from an image, the FT image initially stays linked to the source image. Click this button to remove the link.
	Autorotation	Click this button to rotate an FT image backwards and forwards by 90°.
	Circle	Use this button to have a circle displayed in the FT image and check the astigmatism correction.
	Load Filters	Click this button to load a saved filter configuration.
	Save Filters	Click this button to save a filter configuration.

(2) The tool window's explorer

In the Fourier Transform tool window's Explorer group you can find all images that are currently loaded in the document group and that are linked to at least one FT image or an IFT image if applicable. The FT and IFT images are arranged below the source images.

What you can do in the document area

Click on one of the entries in the Fourier Transform tool window to activate the FT image, the gray-value image, or the IFT image in the document group. When a lot of images and their corresponding FT images are loaded, this helps you to easily find the images that belong together.

In the above example, three images that have FT images are loaded in the document group

These images are listed in the tree view on the left of the Fourier Transform tool window. On the upper image, two image segments (1) and (2), from which FT images were calculated, are defined. Each FT image is assigned a color in the Fourier Transform tool window. The FT images' tab in the document group's header and the frame in the image segment have the same color.

(3) Fourier filters

In the Filter group in the Fourier Transform tool window, you can define different filters for the computation of Fourier images.

Note: The settings in the Filter group are only available when you've selected an FT image in the document group or in the Explorer group in the Fourier transform tool window.

You can use the filters to accentuate or filter out periodic structures. Define the size of the filter and its other properties and specify how you want the filters to be combined with each other. You can find more information on the individual filters and step-by-step instructions here.

Creating a Fourier filter

Click one of the big buttons in the Filter group to add a new Fourier filter to the active FT image. Several different Fourier filters are available. You will find different settings in the <Name of Fourier filter> settings group depending on which filter is active.

When you add a Fourier filter to the FT image, an IFT image is automatically created and displayed in the document group. The filters effect the IFT image directly so that you can follow the changes in the IFT image in real time.

Fourier filter	Definition	Settings
Bandpass	Define a filter for a specific frequency range. You can use it to filter all periodic structures that have a certain distance to each other out of an image, for example. The frequency range is defined by a circular area in the frequency domain.	In the Lower and Upper fields, you can change the size of the circles. Use the arrow buttons next to the fields or enter a value. Alternatively, you can change the size of the circles interactively in the image window.
Sector	Define a filter for specific orientations in the frequency domain. You can use it to filter specific periodic structures out of an image, only those that run from the bottom left to the top right for example.	In the Orientation field, you can set the angle of rotation used to move the sectors around the center point. In the Opening field, you can change the size of the sectors' angles.
Blob	Define a filter for a very specific frequency and orientation.	In the Orientation field, you can set the angle of rotation used to move the circles around the center point. In the Distance field, you can change the distance between the circles. In the Radius field, you can change the size of the circle.
Lattice	Define a grid shaped filter.	The lattice is defined by two basis vectors. You specify the orientation for each basis vector in the Orientation 1 and Orientation 2 fields. The orientation is determined by the angle between the basis vector and the X-axis, measured clockwise. You can change the length of the basis vectors in the Distance 1 and Distance 2 fields. You can specify the distance between the points in the lattice. In the Radius field, you can change the size of a point in the lattice.
Lattice	The two basis vectors, b1 and b2, define the lattice. The angle between the basis vector and the x-axis (b1=90° and b2 = 310°) specifies the orientation of the basis vectors.

Managing an image's Fourier filter

In the field below, all defined filters are listed. The filters are numbered consecutively, "Annular <consecutive number>" for example. Select or clear the check boxes to activate or deactivate filters. Click the name of the filter to display its filter settings. The corresponding filter settings, <Name of Fourier filter> settings, have the same consecutive number.

Selecting the type of Fourier filter

Select the Inside option if you want the filter range to be inside the circles. The filtered image now only contains the information from the frequency ranges that are outside of the defined filter ranges.

Select the Outside option if you want the filter range to be outside the circles. The filtered image now only contains the information from the frequency ranges that are inside the defined filter ranges. If you want to enhance a periodic structure with a filter, for example, you can define a Fourier filter that contains the frequency range to which this periodic structure belongs and then select the Outside option.

The original image (1) shows a periodic structure that creates point shaped reflexes in the Fourier image (2). A grid shaped Fourier filter has been defined in the Fourier image (2). With the Outside option, the filtered image (3) shows the periodic structures significantly more clearly. This is because all of the frequencies that are outside of the lattice aren't represented in the image any more.

Combining Fourier filters

In the Combination group, select how all of the defined filters are combined with each other. You can select either the Intersection or the Union option.

Select the Intersection option if you only want to take into account the overlapping filter ranges in the transform. The areas that are outside this intersection, are not taken into account by the transform.

Select the Union option if you want to combine the ranges of all of the filters with each other. The range of all of the filters will be taken into account by the transform.