MOIRÉ PATTERNS FROM A CCD CAMERA

Are They Annoying Artifacts or Can They be Useful?

Tong Tu and Wooi-Boon Goh

School of Computer Engineering, Nanyang Technological University, Singapore 639798, Singapore

Keywords: Moiré pattern analysis, Image-based metrology, Surface reconstruction.

Abstract: When repetitive high frequency patterns appear in the view of a charge-coupled device (CCD) camera,

annoying low frequency Moiré patterns are often observed. This paper demonstrates that such Moiré pattern

can useful in measuring surface deformation and displacement. What is required, in our case, is that the

surface in question is textured with appropriately aligned black and white line gratings and this surface is

imaged using a grey scaled CCD camera. The characteristics of the observed Moiré patterns are described

along with a spatial domain model-fitting algorithm that is able to extract a dense camera-to-surface

displacement measures. The experimental results discuss the reconstruction of planar incline and curved

surfaces using only a coarse 33 lines per inch line grating patterns printed from a 600 dpi printer.

1 INTRODUCTION

Moiré patterns are the results of the interference

fringes produced by superimposing two sets of

repetitive gratings. These patterns are used in

metrology for tasks such as strain measurements,

vibration analysis and the 3D surface reconstruction

(Kafri, 1990), (Walker, 2004), (Creath, 2007). Moiré

images are normally obtained using a camera to

capture the patterns generated by superimposing two

alternating opaque-transparent Ronchi gratings

(Khan, 2001) or two projected light patterns.

In this work, the imaging device itself plays the

role of one of the grating with its regular 2D

repetitive arrangement of charged-coupled cell

arrays. This camera is then used to observe another

grating. The interaction between the two ‘gratings’

results in the formation of Moiré patterns, which can

be simply captured by the CCD camera itself. This

imaging device-based approach of using Moiré

fringes for surface displacement measurement was

suggested by (Chang, 2003), where they

demonstrated how wavelet transform (WT) could be

used to extract the pitch of the Moiré fringes for

micro-range measurement. A micro-pitch grating of

300 lines per inch (lpi) was employed as the

specimen grating so that the pitch dimensions of the

grating is close to that of the CCD cell spacing. This

situation produces Moiré fringe patterns (see Fig. 2)

that do not suffer annoying artufacts, making it

relatively easy to extract the peak-to-peak fringe

pitch. Unfortunately, peak-to-peak pitch values are

only useful in providing distance measurements of

flat surfaces perpendicular to the imaging plane.

Their approach cannot be readily used to generate a

dense varying depth map of the surface.

We propose using specimen grating with

relatively larger pitch (≤ 33 lpi), which can be easily

printed with a 600 dpi laser printer. Unfortunately,

such coarse pitch result in Moiré patterns that

contain high frequency artifacts (see Fig. 3b), which

embeds the desired Moiré fringe waveform. We

discuss some property resulting from employing the

CCD array as a reference grating that allows these

artifacts to be easily removed. We also present a

spatial domain model-fitting algorithm for

measuring the instantaneous pitch width of the

Moiré fringes, thus allowing the reconstruction of

dense depth profiles.

2 THE MOIRÉ PATTERNS

2.1 Near Similar Pitch Gratings

Let the pitch width of the reference and specimen

gratings be p

and p

respectively. In Fig. 1(a), we

have a situation where the pitch of p

> p

, but only

slightly. As a result, lower frequency Moiré fringes

(light) with period p

results due to the repeated and

Tu T. and Goh W. (2009).

MOIRÉ PATTERNS FROM A CCD CAMERA - Are They Annoying Artifacts or Can They be Useful? .

In Proceedings of the Fourth International Conference on Computer Vision Theory and Applications, pages 51-58

DOI: 10.5220/0001807700510058

 SciTePress

regular maximum overlap of the two sets of dark

lines. Dark fringes are observed in zones of

minimum overlap. Assuming no relative rotation

between the two line gratings, the Moiré fringe

pitch, p

is given by the well known equation [6]

−

(1)

Reference line grating

Moiré frin

itch,

Specimen line grating

(a)

1 2

3 4

’= p

+ p

Moiré fringe pitch, p

’

rrs

ppp <−

(b)

rrs

ppp >−



Figure 1: Resulting pitch for the Moiré fringes generated

when the specimen grating pitch is (a) only slightly larger

than the reference grating pitch and (b) much larger than

the reference grating pitch. Notice the Moiré fringe pitch

is made up of k = 3 specimen grating pitches in both cases.

Assume the reference line grating is now

replaced by a regular-pitched CCD imaging cells.

Fig. 2a shows the resulting 1-D image intensity

profile. Notice that the extracted period p

of the

Moiré fringe pattern can be easily obtained as there

are no specimen line grating artifacts, as observed

with the 300 lpi line gratings used in (Chang, 2003).

(b)

Specimen grating

(

)

Moiré fringe pattern

Image Intensity

CCD cells

Equi-spaced CCD cells

2 4 6 8 1

Moiré fringe pattern

Image Intensity

CCD cells

= 40, p

=46 p

= 40, p

=48



Figure 2: Moiré fringe patterns obtained when using point

spread integration of the specimen grating intensity falling

on regularly-spaced CCD cells. The image intensity

profile obtained when the CCD pitch (reference grating)

and the specimen line grating pitch are (a) p

= 40,

= 46 and (b) p

= 40, p

= 48 spatial units respectively.

As given in eqn. (1), the further p

is from p

, the narrower

is the Moiré fringe pitch p

2.2 Larger Pitch Gratings

What happens when the pitch of the specimen

grating, p

is much larger than that of the reference

grating, p

, as shown in Fig. 1b? We now derive a

new expression for the Moiré fringe pitch, p

′ for

the situation shown in Fig. 1b where

rrs

ppp >−

since the fringe pitch expression given in eqn. (1) is

only valid for the situations shown in Fig. 1a, where

rrs

ppp <−

. In order to make use of eqn. (1), we

need to subtract the largest integer multiple of the

reference pitch p

from the large specimen line

grating pitch p

′. The remaining pitch value after

subtraction, given by

is less than p

and can

therefore be substituted into eqn. (1) to compute the

Moiré fringe pitch p

. In Fig. 1b, we illustrate an

example where this remaining pitch

is similar to

the specimen grating pitch p

in Fig. 1a. As shown in

Fig. 1a, if the width of the Moiré fringe pitch p

made up of k × p

width (example in Fig 1 has k =

3), then the fringe pitch p

′ of the wide specimen

grating will also be given by k × p

′. From eqn. (1),

the number of specimen line grating, p

making up

the Moiré fringe pitch width, p

is given by

−

(2)

If p

′>>p

, we need to find the maximum number

of integer multiples of p

within p

′ given by

⎥

⎦

⎥

⎢

⎣

⎢

(3)

where ⎣⎦ is a flooring function. The remaining

pitch

)

after removing multiples of p

is given by

rss

mppp −= '

],0[

p∈

(4)

The number of specimen line grating pitch width

contained within the Moiré fringe pitch can be

obtained by substituting (4) into (2), and is given by

−

′

(5)

We can now compute the Moiré fringe pitch, p

′

for the large specimen line grating with pitch p

′

from eqns. (4) and (5) and this is given by

')1(

ppm

pkp

−+

−

=×

′

(6)

From this general expression of the Moiré fringe

pitch, we can observe that the presence of the (1+m)

VISAPP 2009 - International Conference on Computer Vision Theory and Applications

factor ensures that the absolute value of the

denominator of both eqns. (1) and (6) will not

exceed 1. This means the increase in specimen

grating pitch p

′ will produce a fringe pitch p

′ that

is equally magnified, as shown in Fig. 3b.

2.3 Removing Grating Artifacts

5 10 15 20 25 30 35 40

(b)

Specimen line gratings

(

)

Moiré frin

e pattern

Image Intensity

CCD cells

Moiré fringe pattern

CCD cells

′

=40, p

=48

=40, p

=88

5 10

20 25 30 35 40

....................

Equi-spaced CCD cells

Figure 3: 1D Moiré fringe patterns obtained with specimen

line gratings of different pitch widths. In both cases, the

reference grating p

= 40. Specimen line grating pitch in

(a) p

= 48 and in (b) p

= 88, (i.e. m = 1). In both cases,

the remaining pitch widths

The resulting Moiré pattern produced when m >1

(see Fig. 3b) contains high frequency artifacts from

the specimen line grating, which, makes automatic

fringe pitch estimation difficult.

5 10 15 20 25 30 35 40

0.2

0.4

0.6

0.8

2 4 6 8 10 12 14 16 18 20

0.2

0.4

0.6

0.8

Ima

e Intensit

After sub-sampling every other even pixel intensity value

Ima

e Intensit

Full resolution Moiré pattern

11 pixels

Figure 4: Removing line grating artifacts by sub-sampling.

Notice the pitch width (i.e. 11 pixels) of the Moiré fringe

remains unchanged after sub-sampling.

Since the reference grating pitch p

is the pitch of

the CCD cell and therefore the pixel width, we can

quickly remove these high frequency artifacts by

sub-sampling the Moiré pattern waveform as shown

in Fig. 4. For situations where m =1, down-sampling

is done by selecting every other pixel in the original

N × N sized image to form new image of size

N/2×N/2. It is unimportant whether the even or the

odd pixels are removed as this only results in a

phase shift. When the value of (1+m) in eqn. (6) is

3, we can obtain an artifact-free waveform by sub-

sampling every other 3

pixel. When (1+m) is 4, we

sub-sample every other 4

pixel and so on.

Given that the true pitch of the specimen grating

is given by S. If we assume a thin lens (pin-hole)

camera model and the distance of the surface of the

specimen to the centre of projection given by d is

relatively larger than the focal length of the camera

given by f, the specimen grating pitch p

′ can be

approximated by

(7)

Putting (7) into (6) and rearranging, we get

⎟

⎠

⎞

⎜

⎝

⎛

ppm

)1(

(8)

Given that f, S, and p

are constants, the distance d

from the camera has an inversely proportional

relation to the measure Moiré fringe pitch, p

′.

2.4 CCD Cell Summation Model

The observed Moiré pattern is formed from the

accumulation of individual CCD cell summation of

the specimen line grating intensities. But how would

the intensity summation model influence the shape

of the resulting Moiré waveform? We obtained

simulation results for three hypothetical summation

models (see Fig. 5), namely impulse, Gaussian and

uniform. Fig. 6 shows the resulting 1D Moiré pattern

waveform for each of the summation models. Notice

that the shape of the waveform is dependent on the

CCD integration function but the fundamental

frequency, which is related to the Moiré fringe pitch

width, remains unchanged.

10 15 20 25 30 35 40

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Gaussian

Impulse

Unit

Figure 5: Three different intensity summation models for

the hypothetical CCD cell.

From eqn. (8), the pitch period of the sub-

sampled Moiré waveform provides a reciprocal

description of the surface displacement d from the

camera. As such, the instantaneous frequency (i.e.

reciprocal of pitch) of the fundamental sinusoid of

the waveforms shown in Fig. 6 will allow us to

reconstruct a dense surface depth profile along a

MOIRÉ PATTERNS FROM A CCD CAMERA - Are They Annoying Artifacts or Can They be Useful?

selected 1D cross-section of the Moiré image. This

is achieved independently of the assumed CCD cell

summation model. We next describe an algorithm to

extract the instantaneous frequency of a 1D sub-

sampled Moiré pattern waveform.

(a)

(b)

5 10 15 20 25 30

(c)

Gaussian

Impulse

Uniform

Figure 6: The resulting Moiré waveform using (a)

Gaussian point spread, (b) impulse and (c) uniform CCD

cell intensity summation model.

3 EXTRACTING DEPTH

Fig. 7(c) shows the sub-sampled waveform obtained

from a 1D cross-section of a Moiré pattern image

obtained for a curved line grating surface. The

varying intensity could be due to shadows or uneven

ambient lighting during imaging.

200 400 600

100

150

200

250

image intensity

pixel

position

0 20 40 60 80 100 120 140 160

100

150

200

250

Down-sampled waveform, s(n)

Moiré pattern image

Waveform at cross section

Sub-sample every

other 4

pixel

pixel position (n)

image intensity

(a)

(b)

(c)

Figure 7: (a) Moiré pattern image of a curved line gating

surface acquired under uneven lighting condition. (b) The

full resolution intensity profile along the dotted (red)

cross-section. (c) The waveform with the line grating

artifact removed by sub-sampling every other 4

pixel in

the original 1D cross section of the Moiré pattern image.

Notice that the sub-sampled waveform s(n) in

Fig. 7(c) can be viewed as a multi-component time-

varying amplitude and frequency modulated (AM-

FM) signal that is riding on a time-varying bias. In

order, to extract the varying pitch period of the

signal, we need to extract the instantaneous

frequency of the fundamental sinusoid taking into

account the varying bias and amplitude of the signal.

We modelled the fundamental AM-FM sinusoid by

modifying the least-squares truncated power series

approximation (L-STPSA) model approach of (Goh

2007) with an additional time-varying bias. Firstly,

the sub-sampled waveform s(n) is converted to a

positive-negative going zero-mean signal x(n) using

∑

−=

nsnx

)(

)()(

(9)

3.1 The L-STPSA AM-FM Model

An AM-FM sinusoidal signal

()xn

with a varying

bias given by v(n) can be represented by

)()](cos[)()(

nvnnwnAnx

(10)

where w

is a fixed carrier frequency with

varying amplitude A(n). The instantaneous

frequency f(n) is the derivative of the varying phase

(n) and is given by

])([

)(

dnndw

(11)

The signal x(n) can be expanded to its in-phase

and quadrature sinusoidal components given by

(

)

(

)

[

]

(

)()

[]

)(sincos)(

nvnnwnbnnwnanx

++++=

θθ

(12)

where a(n) and b(n) are given by

))(cos()()( nnAna

and

))(sin()()( nnAnb

−=

(13)

If we assume the functions that describe the

varying amplitude A(n) and phase

(n) are analytic,

then such functions can be approximated by a power

series. As an example, cos x is given by the series

...!6!4!21cos

642

−+−+−= xxxx

(14)

We can now model the components of

()xn

and

the varying bias v(n) as general truncated power

series of orders P and R respectively, given by

∑

anna

)(

∑

bnnb

)(

∑

vnnv

)(

(15)

The modelling process starts by assuming there

are no phase variations (i.e.

(n) = 0). Then, given a

signal x(n) of sample length N, the modelled signal

()xn

in eqn. (10) can be estimated by minimising the

mean squared-error

in (16) with respect to the

(P+1) pairs of amplitude coefficients, the (R+1) bias

coefficients and predetermined carrier frequency w

)}()(

{ nxnx

−=

∑

(16)

VISAPP 2009 - International Conference on Computer Vision Theory and Applications

Here, the coefficients estimation in (Goh, 1998)

is extended with a further (R+1) equations to solve

for the varying bias v(n). Since the varying phase is

estimated iteratively, it is not important what the

predetermine carrier frequency w

is as long as it is a

frequency component present in the waveform. We

chose w

by picking the frequency corresponding to

the highest peak frequency in the power spectrum of

the waveform x(n). (Goh, 2007) showed that the

current estimate of the varying phase is given

()

() ()

⎥

⎦

⎤

⎢

⎣

⎡

+−

)(sin)()(cos)(

arctan

nnbnna

nnannb

θθ

(17)

From eqn. (15), both a(n) and b(n) can be

estimated from the (P +1) a

and b

coefficients

using the L-STPSA model of order P. With initial

values of

(n) = 0, we make an initial estimate of the

varying phase

()

using eqn. (17). The phase is

then unwrapped by tracking the 2π jumps in its

values and then parameterised using another L-

STPSA model of order Q given by

()

∑

ncn

(18)

The smooth L-STPSA reconstructed phase

function

(n) in (18) is then substituted back into the

AM-FM signal model in (12) to obtain another new

estimate of a(n) and b(n), which in turn is

substituted, along with

(n), into (17) to compute a

new estimate of the varying phase

(

)

. This

iterative parameter-substitution process is repeated

until the waveform model in the M th iteration

deviates little from that estimated in the (M+1)th

iteration. Fig. 8 shows the progressive sinusoidal

signal estimation. For the waveform shown in Fig.

7(c), reasonable convergence occurred after the 6

iteration, with P = 12, Q =5, R =3 and w

= 0.393.

pixel position (n)

zero mean intensity

(a)

(b)

0 20 40 60 80 100 120 140 160

-50

100

150

0 20 40 60 80 100 120 140 160

-50

100

150

pixel position (n)

zero mean intensity

Iteration #1

Iteration #6

reconstructed sinusoid

original signal

varying intensity bias

Figure 8: (a) The estimated L-STPSA AM-FM sinusoid of

the fundamental frequency at (a) iteration #1 and (b) at

stable full signal reconstruction at iteration #6. The

original waveform and estimated varying bias is shown in

dotted (red) and dashed lines (black) respectively.

Once a stable AM-FM sinusoid has been

iteratively estimated, the varying phase

(n) from

(18) can yield an instantaneous frequency as given

in (11). Since we are interested in the varying pitch

period of the Moiré pattern, we can relate the

varying phase

(n) in (18) to the reciprocal of the

Moiré pattern pitch width p

′ in (8) using the

instantaneous frequency given in (11)

θθ

)1()(

)(

)('

−−+

nnw

(19)

The derivative of the varying phase in (11) is

approximated using backward difference. Fig. 9

shows a 1D depth profile of the line grating surface

shown in Fig. 7(a), obtained from the plot of 1/p

′(n)

in (19) using the fundamental sinusoid’s estimated

phase changes shown in Fig. 8(b).

0 20 40 60 80 100 120 140 160

pixel position (n)

′

camera distance, d

Figure 9: The cross-sectional profile of the distance

between surface and camera computed from the

instantaneous frequency estimate of the recovered L-

STPSA sinusoidal signal in Fig. 8(b).

4 EXPERIMENTAL RESULTS

4.1 Experimental System Setup

The experimental setup used is shown in Fig. 10. It

consists of a CCD camera mounted on a crank-

based height-adjustable stand, a personal computer

(PC) and A4-sized white paper with uniform black-

white line gratings printed from a 600dpi laser

printer. The camera is the Dragon Fly Express

monochrome model (PointGrey, 2008) from Point

Grey Research Inc., with a C-mount lens of focal

length 25mm. The resolution of the captured image

is 640 × 480 pixels.

Paper with line grating patterns

Personal

computer

Height-adjustable

camera stand

CCD camera

1D cross section

(perpendicular to

line gratings)

Figure 10: The basic experimental setup.

MOIRÉ PATTERNS FROM A CCD CAMERA - Are They Annoying Artifacts or Can They be Useful?

The distance, d from the camera imaging plane to

the line grating surface is proportional to the inverse

of Moiré fringe pitch width, 1/p

′ and this width is

related to the instantaneous frequency of the Moiré

waveform as shown in (19). In other words, the 1D

distance profile along the cross section shown in Fig.

10 can be generalized to

bnkfb

knd

+=+×= )(

)('

)(

(20)

where k and b are unknown system constants.

The instantaneous frequency f(n) given in (19) is

computed from the extracted L-STPSA fundamental

sinusoid of the 1D Moiré pattern waveform.

The first experiment verifies that the distance

from the camera, d is proportional to the extracted

instantaneous frequencies, f of the fundamental

sinusoid of the 1D Moiré pattern waveform. The L-

STPSA model parameter values of P =5, R =3 and

Q = 2, as given in eqns. (15) and (18) was used. By

setting Q = 2, we are adopting a constant phase

model as we do not expect the frequency of the

Moiré pattern to change over the 1D cross section

since the distance, d to the surface is much larger

that the focal length, f of the camera lens.

Fig. 11 shows the results obtained for the d

distances from 70.0cm to 75.0cm, in steps of 0.5cm.

At this distance and with the printed line grating

pitch used, the value of m in (3) is 3 and artifact-free

1D Moiré waveform is obtained by sampling every

other 4

pixel of the original resolution waveform.

Notice that the results obtained in Fig. 11 confirm

the proportional relationship given in (20).

measured data

best linear fit

0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1

70.5

71.5

72.5

73.5

74.5

distance to camera,

instantaneous fre

uenc

Plot of distance versus instantaneous frequency

Figure 11: A plot to show the relationship between the

distance, d between the line grating surface and the CCD

camera and the estimated instantaneous frequency, f of the

Moiré pattern waveform.

4.2 1D Incline Planar Surfaces

This experiment demonstrates the use of the AM-

FM modelling property of the L-STPSA technique

to estimate the changing instantaneous frequency of

the Moiré pattern waveform across the 1D cross

section. By using an incline line grating surface, the

distance to the camera would vary linearly from one

end of the 1D cross section (see Fig. 12) to the other.

CCD

camera

(a)

(b)

Line

grating

Image acquired

Figure 12: (a) Experimental setup for the incline planar

surface analysis. (b) The acquired image with the dashed

line (blue) indicating the 1D profile used in the analysis.

Fig. 13(a) shows the Moiré pattern waveform

obtained for a planar incline of about 10 degrees.

Fig. 13(b) shows the corresponding frequency-

varying fundamental sinusoid estimated using the L-

STPSA model parameters of

P =5, R =3 and Q =5.

The linearly changing chirp-like instantaneous

frequency fundamental sinusoid can be seen in the

Moiré waveform shown in Fig. 13(b).

pixel position (n)

zero mean intensity

(a)

(b)

zero mean intensity

20 40 60 80 100 120

-50

20 40 60 80 100 120

-50

reconstructed fundamental sinusoid

Original Moiré waveform

pixel position (n)

Moiré waveform

amplitude envelope

varying intensity bias

Figure 13: (a) The Moiré pattern waveform obtained from

an incline line grating. Also shown is the estimated

amplitude envelope for the fundamental sinusoid and the

varying bias. (b) The extracted fundamental sinusoid of

the Moiré waveform using the L-STPSA modelling

technique. Shown in dotted line (red) is the error residue

between the estimated sinusoid and the original signal in.

Fig. 14 shows the plot of the instantaneous

frequency of the fundamental sinusoid in Fig. 13(b).

Observe that the extracted instantaneous frequency

varies closely to that of an incline, as we would

expect from the proportional relationship between

distance,

d and instantaneous frequency, f in (20).

VISAPP 2009 - International Conference on Computer Vision Theory and Applications

20 40 60 80 100 120

0.05

0.06

0.07

0.08

0.09

0.1

0.11

pixel position (n)

instantaneous frequency, f

frequency, f

best incline fit

Figure 14: The incline observed in the instantaneous

frequency, f is plotted against a best fit incline.

4.3 2D Incline Planar Surfaces

Next, we imaged a line grating surface that is

inclined in both the x and y directions (see Fig. 15).

We reconstructed a dense surface depth map by

stitching together the all perpendicular 1D cross

sections across the image. Fig. 16 shows the

resulting dense 2D depth map reconstructed by

analysing a series of 1D cross sections.

CCD

camera

multiple 1D

cross sections

Figure 15: The 2D incline surface experimental setup. The

heights h

=64.5 mm, h

=37mm, and h

=33mm.

Figure 16: Reconstructed 2D surface of the incline plane.

4.4 Impact of Uneven Lighting

Conditions

We studied the effects of ambient lighting variations

on the accuracy of the extracted depth using the

proposed CCD Moiré waveform analysis technique.

Fig. 17 shows the setup used in which a curved A4-

sized paper with evenly spaced vertical line gratings

was imaged twice. Firstly, under normal lighting

conditions and secondly, with portions of the line

grating surface covered by shadows.

(a)

CCD camera

Curved surface with

line gratings

(b)

CCD camera

Light

source

Light source

Shadows

added

Occluder

Figure 17: Experimental setup for testing effects of

lighting variations. (a) Normal light source and (b)

Shadows cast on surface due to partially occluded light

source.

Fig. 18 shows the two waveforms obtained after

sub-sampling the intensity value of every other 4

pixel of a 1D cross section. The fundamental

sinusoidal waveforms along with their respective

instantaneous frequencies were extracted for both

waveforms using

P =10, Q =5 and R =3. The

carrier frequencies used in Fig. 18(a) and 18(b) were

= 0.668 and w

= 0.628 respectively.

The resulting 1D depth profiles of the surface

cross section under different lighting conditions

were plotted together as shown in Fig. 19. Hardly

any noticeable variations in depth profiles were

observed. This shows that the proposed technique

for measuring the depth profile of a line grating

surface is robust to lighting variations. The ability of

the L-STPSA technique to simultaneously extract

the varying instantaneous frequency and amplitude

modulation envelopes in a waveform allows us to

handle changes in the Moiré pattern intensity, which

does not fundamentally change the pitch of the

Moiré fringes.

pixel position (n)

zero mean intensity

(a)

(b)

pixel position (n)

zero mean intensity

20 40 60 80 100 120 140 160

-100

-50

100

20 40 60 80 100 120 140 160

-100

-50

100

Normal lighting

With shadows

Moiré waveform

Estimated AM

varying intensity bias

Figure 18: The 1D intensity profiles of the sub-sampled

zero-mean Moiré pattern waveforms obtained under (a)

normal lighting condition and (b) with shadows. Notice

the shadows resulted in uneven intensity attenuation. The

estimated amplitude modulation envelopes of the

MOIRÉ PATTERNS FROM A CCD CAMERA - Are They Annoying Artifacts or Can They be Useful?

fundamental sinusoids are shown dotted (red) and the

varying biases are shown in dashed lines (black).

pixel position (n)

Camera distance, d

0 20 40 60 80 100 120 140 160

1D depth profiles

Normal lighting

With shadows

Figure 19: The plot of the two estimated 1D depth profiles

of Moire pattern waveforms in Figure 19(a) and 19(b).

The two overlapping profiles are almost identical despite

the significant variation in the intensity profile.

5 CONCLUSIONS

We introduced a method of measuring dense 2D

surface depth maps using the Moiré patterns

captured from a CCD camera. This uniform CCD

cell array is exploited in the generation of the Moiré

patterns, making this approach simpler and less

expensive than the use of Ronchi gratings. A novel

sub-sampling technique was introduced to remove

artifacts that resulted from adopting a more

convenient and inexpensive setup in which larger

specimen line grating pitch width were be employed.

A spatial domain parametric technique was

proposed for extracting the instantaneous frequency

of the Moiré pattern waveform and we showed that

this frequency parameter is proportional to the

surface-camera distance and can therefore be used to

analyse the relative depth variation of the line

grating surface. We also showed that the depth

profiles estimated from the observed Moiré pattern

are independent of the intensity variations over the

line grating pattern, which makes such measurement

techniques easy to deploy under conditions that

consistent and uniform lighting cannot be assured.

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Walker, C.A. (Ed), 2004, Handbook of Moiré

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Point Grey Research Inc., 2008, Dragonfly Express,

http://www.ptgrey.com/products/dx/dx.pdf

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