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SEMI T10-0701 © SEMI 2001 6 7.4 Mark Growth 7.4.1 Ma rk Gro wth is co ncer ned wit h t ra cki ng the tend ency of a ma rking s yste m to o ver o r under mark t he symbol. This is a size com p arison between the actual ma…

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

SEMI T10-0701 © SEMI 20017

7.5.3 Data Matrix Cell Height

7.5.3.1 Compute the Data Matrix Cell Height

(DMCH) using the distance between P1 and P2,

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

dist(P3,P4) and the number of rows M as follows:

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

DMCH

(6)

Report the Data Matrix Cell Height.

7.6 Data Matrix Mark Misplaceme nt

7.6.1 Data Matrix Mark Misplacement measures the

average misplacement of Data Matrix marks from their

respective ideal Data Matrix Cell Center Points as

defined in Section 7.1.3. The Mark Misplacement is

measured separately in horizontal and vertical

directions relative to the average width of the marks in

the respective direction.

7.6.2

Using the mark cell horizontal and vertical edge

locations, as determined in Section 7.4.2, compute the

image coordinate of the midpoint between the edges of

each mark in the corresponding horizontal and vertical

directions. In the horizontal direction, for each mark

calculate its misplacement MH

as the distance between

the detected midpoint and its ideal cell center point. In

the vertical direction, for each mark calculate its

misplacement MV

as the distance between the detected

midpoint and its ideal cell center point.

7.6.3

Horizontal Mark Misplacemen t

7.6.3.1 In the horizontal direction, for a given number

of columns N, and the Data Matrix Cell Width

(DMCW) as computed in Section 7.5.2, compute the

Horizontal Mark Misplacement (HMM)as follows:

100%

DMCWn

HMM ×

= (7)

where n = N/2 if N is even or n = N/2+1 if N is odd.

Report the Horizontal Mark Misplacement.

7.6.4

Vertical Mark Misplacement

7.6.4.1 In the vertical direction, for a g iven number of

rows M, and the Data Matrix Cell Height (DMCH) as

computed in Section 7.5.3, compute the Vertical Mark

Misplacement (VMM) as follows:

100%

DMCHm

VMM ×

= (8)

where m = M/2 if M is even and m = M/2+1 if M is

odd. Report the Vertical Mark Misplacement.

7.7 Unused Error Correction

7.7.1 The error correction capacity of Reed-Solomon

decoding is expressed in the equation:

pdte −≤+ 2

where: (9)

e is the number of erasures,

t is the number of errors,

d is the number of error correction codewords,

p is the number of codewords reserved for

error detection.

7.7.2 Values for d and p are defined by the AIMI

Symbology Specification (often depending on symbol

size), while e and t are determined during a successful

decode. Compute the Unused Error Correction as

follows:

()

100%

2te

1.0UEC ×

−

−=

(10)

Report the Unused Error Correction value.

7.7.3

In symbols with more than one (e.g. interleaved)

Reed-Solomon block, calculate the Unused Error

Correction for each block independently and report the

value for each block.

7.8

Cell Defects and Finder Patter n Defects

7.8.1 If the error correction capacity of the Data

Matrix symbol is not exceeded then the Cell Defect

measurement can be made. Because the Data Matrix

symbol has been decoded, the correct binary value of

each cell is known.

7.8.2

Based upon the Data Matrix Grid as defined in

Section 7.1.2 (Figure 4), and the total matrix size,

identify the number and location of all pixels which fall

within the bounds of the Data Matrix Grid. Based upon

the reflectance threshold determined by the Symbol

Contrast measurement, assign a binary value to each

pixel within the Data Matrix Grid. Accumulate the

total number of identified image pixels, which are the

incorrect binary value. Divide this number by the total

number of pixels within the Data Matrix Grid.

100%

pixelsof#total

pixelsincorrectof#

DefectsCell ×= (11)

7.8.3 Finder pattern quality can be c alculated in a

similar manner. Based on the Data Matrix Grid as

defined in Section 7.1.2 (Figure 4), determine the

number and location of image pixels which fall within

the bounds of the L finder pattern of the Data Matrix

Grid. Using the reflectance threshold determined by

the Symbol Contrast measurement, assign a binary

value to each pixel within the L finder pattern.

Accumulate the total number of identified image pixels,