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SEMI T10-0701 © SEMI 2001 7 7.5.3 Data Matrix Cell Height 7.5.3.1 Compute the Data Matrix Cell H ei ght (DMCH) us ing the distance betw ee n P1 and P2, dist(P1,P2), th e distance betw een P3 and P 4, dist(P3,P4) an d the…

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,

SEMI T10-0701 © SEMI 2001 8

which are the incorrect binary value. Divide this

number by the total number of pixels within the L

finder pattern.

100%

pixelsof#total

pixelsincorrectof#

DefectsF.P. ×= (12)

8 Interpretation of Results

8.1 Result Significance

8.1.1 The significance of the assessment results will

depend on the mark/reader application. Open system

applications in which multiple marker and reader

systems of various types at multiple sites are used will

require stricter adherence to desired mark assessment

results. If the mark is intended to survive subsequent

processing steps after marking which will affect mark

characteristics, then reassessment may be necessary to

ensure continued readability.

9 Reporting Results

9.1 Assessment Results

9.1.1 The results of each assessment shall be reported

and listed individually.

9.2 Additional Information

9.2.1 The following items should als o appear in the

report:

• identification of the mark under assessment;

• operator identification;

•

location of where the assessment was done;

• description of specific marking and reading

equipment used.

9.3 Supplemental Information

9.3.1 Supplemental information can be reported

optionally. This information provides further details

about the size, content and color polarity of the Data

Matrix symbol.

9.3.2

Symbol Type indicates the ECC (error

correction) level of the analyzed symbol. See the AIMI

Specification for details on ECC levels other than ECC

200.

9.3.3

Symbol Size indicates the tota l size of the

matrix, including the L and alternating patterns per the

AIMI specification.

9.3.4 Image Polarity can be Dark on Light or Light on

Dark. The first term refers to the polarity of the L, the

second the polarity of the quiet zone.

9.3.5 Encoded Data shows the printa ble encoded

characters only. As many lines as needed will be

included for larger symbols.

9.3.6

Data Codewords and Error Co dewords (ECC

200 only) shows the actual encoding codewords that are

contained in the symbol. Codewords, which contain

errors, may be indicated or highlighted. By referring to

Annex M of the AIMI Specification the exact physical

location of codewords can be determined.

9.3.7

Encodation Scheme (ECC 0 through 140 only)

reports the “Base” number, which relates to the density

or efficiency with which the data has been encoded in

the symbol. For more detailed information refer to

Section 5 of the AIMI Specification.

10 Precision and Accuracy

10.1 Pixel Resolution

10.1.1 The pixel resolution shall be sp ecified for all

assessments. This value determines the precision,

accuracy and repeatability of each resulting

measurement.

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