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SEMI T10-0701 © SEMI 2001 5 Figure 4 Matrix Cell Center Locations 7.2 Sym bol Contr ast 7.2.1 Symbol Con trast measures the d i stinctiveness of the two reflective states in th e s ymbol, namely light a nd dark. Many asp…

SEMI T10-0701 © SEMI 2001 4

7 Procedure

7.1 Location and Orientation of the Data Matrix

Symbol

7.1.1 Data Matrix Location Descrip tors

7.1.1.1 The implementation of the symbol quality

assessment depends on knowledge of the location and

orientation of the Data Matrix symbol in the image,

which consists of the 4 image coordinate values of the

matrix corner points, P1, P2, P3, and P4 (see Figure 3).

In addition, the number of rows M and the number of

columns N in the Data Matrix symbol is also required

(see Figure 3). Determine the image coordinate values

and the number of rows and columns using a pre-

processing decoding procedure resident in the reading

system. Should this process either fail or not be

available, determine these values by inspection of the

test image. Report the coordinate values of each matrix

corner point and the number of rows and columns.

7.1.2 The Data Matrix Grid

7.1.2.1 Based on the location of the 4 matrix corner

points and the number of rows and columns in the

matrix establish a geometrical 2 dimensional matrix

grid. Establish line segment P1P2 using points P1 and

P2, line segment P2P3 using P2 and P3, line segment

P3P4 using P3 and P4, and finally line segment P1P4,

using P4 and P1. Divide the number of rows M into the

P1P2 line segment, producing M equally sized line

segments. Divide the number of rows M into the P3P4

line segment producing a similar result. Divide the

number of columns N into P1P4 line segment,

producing N equal sized line segments. Divide the

number of columns N into the P2P3 line segment,

producing a similar result. Connect the corresponding

new line segment endpoints between P1P2 and P3P4.

Connect the corresponding new line segment endpoints

between P1P4 and P2P3. This results in a 2

dimensional matrix grid similar to that shown in Figure

3. This grid is generally quadrilateral in shape,

practically rectangular and ideally square.

7.1.3 Data Matrix Cell Center Point s

7.1.3.1 Determine the ideal geometric al center points

in each matrix cell in the following manner. Establish a

new set of points at the bisection of each row and

column line segment used to form the matrix grid.

Form line segments between each corresponding row

bisection point in P1P2 and P3P4. Do the same for the

column bisection points in P1P4 and P2P3. The

intersection points between this new set of lines in each

matrix cell is the ideal geometrical matrix cell center

point (see Figure 4).

Figure 3

Data Matrix Corner Points and Mark Growth Scanline

SEMI T10-0701 © SEMI 20015

Figure 4

Matrix Cell Center Locations

7.2 Symbol Contrast

7.2.1 Symbol Contrast measures the distinctiveness of

the two reflective states in the symbol, namely light and

dark. Many aspects of the mark/reader configuration

affect the resulting symbol contrast in the image.

7.2.2 Within the grayscale image, se lect all of the

image pixels, which fall within the area of the symbol,

extending outward to the limits of any required quiet

zones. Sort the selected pixels by their reflectance

values into a histogram. Calculate the arithmetic mean

of the reflectance histogram. Use this mean value to

separate the reflectance histogram into 2 sections or

sub-histograms, which represent approximate

reflectance histograms for the dark and light contrasts

of the symbol. Calculate the arithmetic mean of each

sub-histogram. The lower grayscale value of the two

means represents the dark grayscale value G

and the

higher value represents the light grayscale value G

Use these two grayscale values to calculate a new

symbol contrast. The difference of the grayscale levels

divided by the full range of grayscale (255 in the case

of 8 bit A/D Sampling) is the Symbol Contrast. Report

the Symbol Contrast value.

100%

Range(255)Grayscale

SC ×

−

= (1)

7.3

Symbol Contrast Signal to Noi se Ratio (SNR)

7.3.1 The Symbol Contrast Signal to Noise Ratio

(SNR) is a relative measure of the symbol contrast

(signal) to the maximum deviation in the light or dark

grayscale level in the symbol (noise). Using the sub-

histograms and the two grayscale values G

and G

found in the Symbol Contrast calculation, calculate the

deviation of each sub-histogram about each respective

grayscale value. Two values will result: the deviation

of light pixels D

and the deviation of dark pixels D

Calculate a symbol contrast difference in grayscale

value using the grayscale values. Divide this contrast

difference by the maximum deviation calculated for the

individual light and dark sections of the histogram.

This ratio is the Symbol Contrast SNR. Report the

symbol contrast SNR.

()

DMax

SNRContrastSymbol

−

= (2)

SEMI T10-0701 © SEMI 2001 6

7.4 Mark Growth

7.4.1 Mark Growth is concerned wit h tracking the

tendency of a marking system to over or under mark the

symbol. This is a size comparison between the actual

marked cells vs. their nominal size. Changes in mark

growth can be indicative of changes in the marking

process or substrate characteristics or changes in the

reader configuration, such as illumination or optical

focus.

7.4.2

Within the grayscale image, ba sed upon the

matrix coordinates and the number of rows and

columns in the matrix, determine a scanline of pixels

which bisects the horizontal alternating pattern and

determine a scanline which bisects the vertical

alternating pattern of the matrix (Figure 3). Scan along

each alternating pattern, generating a cross-sectional

grayscale profile of each alternating pattern as shown in

Figure 5. Determine the location of each edge within

the alternating patterns locally, using an appropriate

edge detection method. Based upon the edge locations,

compute the width of each matrix cell in the horizontal

alternating pattern in the direction of the horizontal

scanline. Also, compute the height of each matrix cell

in the vertical alternating pattern in the direction of the

vertical scanline. Separate the mark and space cell

widths and compute the median space cell width (SCW)

and the median mark cell width (MCW). Horizontal

Mark Growth (HMG) is computed as:

100%

(SCW) Med(MCW) Med

MCW) ( Med

HMG ×

= (3)

Separate the mark and space cell heights and compute

the median space cell height (SCH) and the median

mark cell height (MCH). Vertical Mark Growth

(VMG) is computed as:

100%

Med(SCH)Med(MCH)

Med(MCH)

VMG ×

= (4)

Report the Horizontal Mark Growth and Vertical Mark

Growth values.

7.5 Data Matrix Cell Size

7.5.1 The Data Matrix Cell Size expresses the average

size of each cell in the matrix in pixels and is composed

of a width and height component. Compute the Cell

Size using the distances between corner points and the

known number of rows M and the known number of

columns N in the matrix (referring to Figure 3).

7.5.2

Data Matrix Cell Width

7.5.2.1 Compute the Data Matrix Cell Width

(DMCW) using the distance between P1 and P4,

dist(P1, P4), the distance between P2 and P3, dist(P2,

P3) and the number of columns N as follows:

P3)(P2,dist P4)(P1,dist

DMCW

(5)

Report the Data Matrix Cell Width.

Figure 5

Mark Growth Cross-Sectional Grayscale Profile