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Plane Fit

The Plane Fit command computes a single polynomial of a selectable order for an image and subtracts it from the image. The Plane Fit operation can be applied to either the X, Y, or both XY directions.

Box cursors or passbands allow specific points to be used in the calculation of the polynomial. Click on the image to start drawing a passband box. Right-click on a box to delete it or change its color.

Figure 1 illustrates an image with tilt and bow which could affect the analysis of the surface data.

Figure 1: Visual Representation of Plane Fit

Fitted Polynomials

Refer to Table 1 to view the polynomials that calculate the best plane fit for the images in the Plane Fit Auto function.

Order	Variable	Polynomial Equation
0	X	z = a
	Y	z = a
	XY (Add Higher Order Cross Terms for XY OFF)	z = a
	XY (Add Higher Order Cross Terms for XY ON)	z = a
1	X	z = a + bx
	Y	z = a + by
	XY (Add Higher Order Cross Terms for XY OFF)	z = a + bx + cy
	XY (Add Higher Order Cross Terms for XY ON)	z = a + bx + cy + dxy
2	X	z = a + bx + cx²
	Y	z = a + by + cy²
	XY (Add Higher Order Cross Terms for XY OFF)	z = a + bx + cy + dxy + ex² + fy²
	XY (Add Higher Order Cross Terms for XY ON)	z = a + bx + cy + dxy + ex² + fy²+ gxy² + hx²y + ix²y²
3	X	z = a + bx + cx² + dx³
	Y	z = a + by + cy² + dy³
	XY (Add Higher Order Cross Terms for XY OFF)	z = a+ bx + cy + dxy + ex² + fy² + gxy² + hx²y + jx³ + ky³
	XY (Add Higher Order Cross Terms for XY ON)	z = a + bx + cy + dxy + ex² + fy²+ gxy² + hx²y + ix²y² + jx³ + ky³ + lxy³ + mx²y³ +nx³y³ +ox³y + px³y²

Table 1: Plane Fit Auto Equations

Plane Fit Procedure

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

Figure 2: Select Median from the Workspace

Right-click on a thumbnail in the Multiple Channel window and select Plane Fit

Select Modify > Plane Fitfrom the menu bar.

Click the Plane Fit icon in the toolbar.

The Plane Fit input parameters appear along with the top view image.
Select X, Y, or XY as the Plane Fit Mode.
Select the Plane Fit Order as 0th, 1st, 2nd or 3rd.
Click Execute.
Notice that the image distortion is removed, reflecting a flat, planar profile.

Figure 3: Saddle Image Before Plane Fit

Figure 4: Plane Fit Image

Figure 5: Plane Fit view

Now, experiment with this image to explore the range of Plane Fit capabilities. Try the following:

Change the Plane Fit Order value to see its effects. Notice that there is a vast difference between a value of 1, 2 or 3.
Try plane fitting in one axis (for example, X), but not the other. This generally keeps whatever distortions are presently oriented along the unused axis. For example, the image can be straightened along its Y axis, while leaving the X axis strongly bowed.
Try using a different Plane Fit Order for the X and Y axis (for example, a setting of 3 for X, but a setting of 1 for Y.) This is similar to using one axis, but not the other.
Compare the effect of Plane Fit with Flatten. Notice that each command has a significantly different impact; although, the difference is less noticeable for some types of images.

Plane Fit Interface

A series of parameters appear in the Plane Fit view, allowing the order of the Plane Fit polynomial to be selected and display parameters to be adjusted.

Parameter	Description
Plane Fit Mode	X, Y, XY
Plane Fit Order	Plane Fit Order selects the order of the polynomial calculated and subtracted from each scan line. Settings: 0th—Centers data. 1st—removes tilt. 2nd—removes 2nd order bow. 3rd—removes 3rd order bow.
Plane Fit Z Threshold Direction	Specifies the range of data to be used for the polynomial calculation based on the distribution of the data in Z: Range or Settings: Use Z >= —Uses the data whose Z values are greater than or equal to the value specified by the Z thresholding %. Use Z <—Uses the data whose Z values are less than the value specified by the Z thresholding %. No thresholding—Disables all thresholding parameters.
Plane Fit Z Threshold Percent	Defines a Z value as a percentage of the entire Z range in the image (or data set) relative to the lowest data point.
Add Higher Order	Turning this on adds higher order cross terms to the polynomial fit when XY is chosen (see Table 1).
Output File Name	Specifies the name of the file to be created. Leave blank for immediate view/use without saving the altered image file.
Write File Upon Execute	Writes the output file when the Execute button is clicked.

Table 2: Plane Fit Range, Settings and Buttons

Parameter	Description
Execute	Initiates the Flatten command, based on the order selected..
Reload	Restores the image to its original form by reloading the original file.

Table 3: Buttons on the Plane Fit Panel

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