ST STMPE811 Fiche technique

January 2009 Rev1 1/13

TN0074

Technical note

Calibration procedure for a resistive touchscreen

system based on the STMPE811

Introduction

This document describes the calibration procedures for a resistive touchscreen system

based on the STMPE811 8-bit port expander with advanced touchscreen controller. The

system consists of a screen to display information to the user, and a touch sensor panel

controlled by the STMPE811 to detect and define the location of a touch event. Each

component has its own resolution and independent coordinate system.

It may not be possible to use the touch coordinates produced by the touchpanel directly as

the screen coordinates. This is because typically there is a mismatch between the two

coordinate systems caused by factors such as mechanical placement error, scale

difference, or the series resistance of the tracks connecting the touchpanel and its driver IC.

A set of transfer functions must be used to convert the touchpanel coordinates to the screen

coordinates. The constants of the functions are defined during the calibration process.

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Contents TN0074

2/13

Contents

1 2-constants calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 3-constants calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

3 Revision history . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

TN0074 2-constants calibration

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1 2-constants calibration

2-constants calibration only corrects misalignment on the X and Y axes, both scaling factor

and offset. Angle misalignment is not corrected. This type of calibration is suitable when the

angle error is negligible (small screen) and a simple calculation is required. The procedure

for 2-constants calibration is quite straightforward.

Figure 1. Mismatch which can be corrected with 2-constants calibration

Point A in Figure 1 is located at coordinate (3,3) on the touchpanel, but on the screen it is

located at coordinate (1.6,1.4). This condition can be corrected using the following transfer

function:

Equation 1

Equation 2

Where:

●YDis the screen's Y value

●XDis the screen's X value

●Y is the touchpanel's Y value

●X is the touchpanel's X value

●a, b, c, d are the transfer function parameters

The two unknowns in both equations can be resolved by choosing two points and defining

them on the screen. For an example, please refer to Figure 2.

AM01966v1

baYYD+=

dcXXD+=

2-constants calibration TN0074

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Figure 2. Example of calibration points

The calibration points are described in Table 1 below:

After the user touches the points on the touchpanel, the panel coordinates are as shown in

Table 2, assuming there is some variation in touch locations.

Only two points are required to solve the equations, but it is recommended to perform the

equations twice and use an average of the results.

In this illustration, there are two groups of equations to be solved. Group 1 is defined as

follows:

Equation 3

Equation 4

Table 1. 2-constants calibration points

Point XDYD

113

211

351

453

Table 2. Input from touchpanel for defined points

Point X Y

11.86.3

21.852.3

39.752.2

4 9.8 6.35

AM01967v1

11D bYaY +=

11D dXcX +=

TN0074 2-constants calibration

5/13

To solve these equations, points 1 and 3 are used:

●Y axis

Equation 5

Solving the matrix results in a1 = 0.487 and b1 = -0.073

●X axis

Similarly, the results are c1 = 0.503 and d1 = 0.095

Group 2 is defined as follows:

Equation 6

Equation 7

Point 2 and 4 are used to solve these equations:

●Y axis

Solving the equation:

Equation 8

●X axis

Solving the equation:

Equation 9

At this point, take an average of the results from the two groups of equations, and this is the

final result of the calibration.

Table 3. Final calibration result using the average of the two point groups

Parameter 1 2 Average

a 0.487 0.494 0.4905

b -0.073 -0.136 -0.1045

c 0.503 0.497 0.5

d 0.095 0.130 0.1125

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1Y 1Y

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12.2 13.6

22D bYaY +=

22D dXcX +=

a2 = 0.494 and b2 = -0.136

c2 = 0.497 and d2 = 0.130

2-constants calibration TN0074

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Hence, the transfer functions from the touchpanel coordinates to the display coordinates

are:

The points chosen for calibration should be capable of representing the entire screen area.

The recommended positions are the corners of the screen, but not too close to the center of

the screen or the borders of the touchpanel. Choosing calibration points too close to the

center results in poor representation of the areas further away from the center. However, if

the points are too near the edges, any mechanical imperfections present in the panel may

affect the result of the calibration.

It is recommended to use points located at 20% and 80% of the X and Y axes, as shown in

Figure 3 below.

Figure 3. Recommended calibration point positions: 20% and 80% of X and Y axes

1125.0X5.0X 1045.0X4905.0Y

−=

AM01968v1

20%

80%

100%

80%

100%

20%

TN0074 3-constants calibration

7/13

2 3-constants calibration

This method of calibration corrects misalignment of the X and Y axes, as well as angle

misalignment. Figure 4 shows an illustration of mechanical misalignment.

Figure 4. Mechanical placement error which includes angle error

Mathematical expressions can be derived from Figure 4. They are:

Equation 10

Equation 11

Introducing a scale difference between the panel and the display, we have:

Equation 12

If an error is introduced in the X and Y axis (represented by XTand YT) of Equation 12, the

resulting equation is:

Equation 13

Using trigonometric identity with the assumption that ∆θ → 0, the result is:

Equation 14

and Equation 13 can be modified to:

AM01969v1

Δθ

,YD)

(X,Y)

()

[]

θθ= sinR,cosRY,X

() ()()

[]

θ∆−θθ∆−θ= sinR,cosRY,X DDDD

( ) () ()

[]

θ∆−θθ∆−θ= sinRK,cosRKY,X YXDD

( ) () ()

[]

TYTXDD YsinRK,XcosRKY,X +θ∆−θ+θ∆−θ=

()

θ−θθ∆=θ∆−θ

θθ∆+θ=θ∆−θ

sincos)sin( sincoscos

3-constants calibration TN0074

8/13

Equation 15

Equation 16

To simplify the equations, Equation 15 and 16 can be rewritten as:

Equation 17

Equation 18

It is clear that to solve Equation 17 and 18, at least 3 points are required. The points used

must be independent of each other (not in a straight line).

The 3 independent points chosen are illustrated in Figure 5. The coordinate (XDn,YDn)

contain the chosen points of the screen coordinate, while (Xn,Yn) represents the user’s

input on the touchpanel corresponding to the points displayed on the screen.

Figure 5. Example of 3 independent points

The matrix representation is as follows:

Equation 19

TXXD XsinRKcosRKX +θθ∆+θ=

TYYD YsinRKcosRKY +θ−θθ∆=

CBYAXXD++=

FEYDXYD++=

AM01970v1

(X1,Y 1)

(X2,Y 2)

(X3,Y 3)

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1YX 1YX 1YX

TN0074 3-constants calibration

9/13

Equation 20

The unknown can be calculated using the equations that follow.

Equation 21

Equation 22

where

and

To increase accuracy, more points can be used to solve the equation. An example 5-point

calibration is shown below. Similar to 3-point calibration, a matrix representation is formed:

Equation 23

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1YX 1YX 1YX

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1YX 1YX 1YX

() ()

MAdj

det1

−

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×=

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3-constants calibration TN0074

10/13

Equation 24

where

Equation 23 and 24 are solved by multiplying both sides by (MTxM)-1x MTto get:

Equation 25

Equation 26

To simplify, the values of the unknowns are calculated as follows:

Equation 27

where

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1YX 1YX 1YX 1YX 1YX

()

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×××=

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−

AMMM

()

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×××=

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−

DMMM

d/dF d/dE d/dD d/dC d/dB d/dA

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