Shimizu, Eiji

Takahasi, Hideya

Yamada, Kenji

Osaka City University Repository

(3)
Mem. Fac. Eng., Osaka City Univ., Vol. 38, pp. 7 -14 (1997)
Extracting Three-dimensional Information with Complex Amplitude
- Pattern Matching using a Hologr.aphic Method-
Kenji YAMADA*, Hideya TAKAHASHI** and Eiji SHIMIZU***
(Received September 30, 1997)
Synopsis
We worked on a lnethod for. extracting thr.ee-diInensional inforlnation froln holographic interfer.ence
fringe patterns by using an interfer0111eter. So far, we identified the matching Inethod by using the SUIn
of products and the method that used an optical correlation systeIn, we made a lot of Inasks for. the depth
direction and had to exchange theIne In ~he work described in this paper, we used only one Inask as complex
aInplitude distribution instead of the aInplitude distribution. Her.e we present the Ine~hod that extracts
three-dilnensional inforluation by sifting the plane of observation phase information data with the
iInproved optical corr.elation systeln.
KEYWORDS: holography, thr.ee dimensional inforll1ation extract, optical correlation
Intr.oduction
Recently three-dimensional computer graphics and virtual reality have been studied, and we expect much fom three
dimensional display. As especially animation developed using holography, which can display natural three dimensional
inlages, three dimensional input and measure technique beCalnelTIOre necessary!):. So, we supposed an optical method for
extracting three dimensional infOrmation ofan object surface using a CCD with holography, which SHIRAI supposed in
ultrasound2 f.
So far, we identified the 111atching 111ethod by using the SUll1 of products and the ll1ethod that used an
optical correlation systelu, we ll1ade a lot of 111asks for the depth direction and had to exchange them. In
the work described in this paper, we used only one n1ask as complex amplitude distribution instead of the
alnplitude distribution.
Here, we present the method that extracts three-dill1ensional information by sifting the plane of
observation phase inforlllation data with the ill1proved optical correlation system.
We can collect based patterns to only one by shifting observation data plane with complex
a1l1plitude pattern 111atching. Then, the 1l1any ll1e1l10ry beco1l1e needless and the pl'ocessing time is
shortened. Therefore, we can correct the weak point of the for1l1er ll1ethod.
The principle of extr.acting thr.ee-dimensional information
The optical layout for measuring three dimensional infonnation is shown in Figure 1. First, the plane wave incident the
object in the observation space. The phase of the object bealn and the one ofthe referencebeamintetfereas the surface ofthe
object is the point source. On the CCD camera, the light intensity is taken as tlrree dimensional infolmation. On Figure 1,
the complex amplitude distribution of the object O(ln,n) is;
0(111,n) = U(ln,n) exp{jrPo (rn, n)} (1)
where m,n is coordinates, U(m,n) is amplitude on the CCD and cb o(m,n) is the phase distribution of the point sources.A
is the amplitude ofthe reference beam fOlm the point sources. r(m,n) is the distance fom the point sources to the coordinate
on the CCD. A is wave length. Then, U(111,n) is expressed as U(m,n)=Nr(m,Jl) and cb o(m,n) is done as <b u(m,n)=2
n r(m,n)/ A . The cOlTIplex amplitude distribution of the reference bealn R(ln,n) is;
R(111,n) =Roexp{j rPR} (2)
where Ro is the amplitude of the reference beam, <b R. is the phase of the reference bealTI.
A base pattern for detecting three diinensional infollnation S(m,n) is;
S(m,n) = I(m,n) -IO(m,n)r -IR(m,nt
= 2U(n'1,n)Rocos{rPR.-rPo(n1,n)}
* Student, Doctor Course of Dept. ofElectrical Engineering
** Lecture of Dept. ofElectrical Engineering
*** Professor ofDept. of Electrical Engineering
7
8
where l(m,n) is light intensity ofthe observed interterence fringe pattern on CCD except for the intensity ofobjeet beam and
the one of reference beam.
Next step, we suppose that the smface of the object is the aggregation of the N point sources. The complex amplitude
distribution of the object beam is getting by Huygens - Fresnel principle;
N
O(nt,n) = L: U(i,tn, n)exp {j <Po (i,ln, n)} (4)
i=l
(6)
(5)
where Ui, Ai, ri, ¢ oi is the variable of the each point sources.
The observed data ( hologram illfolmation) of the object in any place is;
g(m,n) = l(m,n) -IO(m,n)12-IR(nl,n~2
N
=2U(m,n) Ro L COS {<P R- <Po (i,nt,n)}
i=l
The equation(5) is changed by equation(3) as follow;
N
g(nt,n) = 2U(nt,n)R o LCOS{<PR- <po(i,nl,n)}
i=1
N
= L:S(i,rn,n)
i=1
We have detected thee dilnensional infonnation by the con-elation between this observed data and any based patten1.
We propose the Inethod that is to get the three ditnensional infonnation by sifting the based pattell1 of the complex
amplitude distribution.
z
r - .- , Observation space
I I
x~~...--yl
~
He-Ne Laser
m IComputer I
Two-dimensional photodetector array
Fig. 1 Optical layout for nleasureing three dimensional infonnation.
The method of detecting thr.ee dimensional information with the complex amplitude distribution pattet·n
1. The p,attern matching with the complex amplitude based pattern
This section shows that the complex alnplitude distribution pattelTI Inatching as well as the amplitude distribution pattern
matching is able to get the three dimensional infonnation.
The observed data on CCD is given by equation(5). This equation is the sum ofthe phase distribution ofthe object beam
include the constant phase ¢ Rand the conjugate phase distribution. Jf ¢ R. is zero;
N
g(m,n) = U(111,n) RoL [expU <P o(i,nl,n)} + exp {-j <Po (i,m,n)}] (7).
i=1
On the old tnethod, this observed data was two dinlensional alnplitude distribution. So, the based patten1 was the
alnplitude distribution as shown equation (3) and we have Inatched by the amplitude distribution. However, the data of
equation(7) include phase infortnation as the cOlnplex alnplitude distribution. Then, we have used the phased distribution
St:(l,ln,n) as shown equation(8) which is expressed for the cOlnplex alnplitude distribution.
Sc (i ,11'2, n) = U (i ,111 , n) exp {j <P (} (i ,In , n) } (8)
We take the thee dimensional infonnation by the cOlnplex alnplitude pattern matching between the based pattern and the
Output plate
P3
9
observed data as shown equation(7). In the case of the cOlnplex amplitude pattern matching, the absolute value of the
complex alnplitude increase in the same complex alnplitude patteln. So, we evaluate the absolute value as the distribution
of the absolute value or light intensity.
2. Optical corr.elation processing with the complex amplitude based pattern
This section show that we have sifted the objective data without changing the based patteln on the optical correlation
systeln, and get the cOlTelation image by the based pattern of each z coordinates.
The optical cOITelation systeln for lneasuring three ditnensional infolmation is shown in Figure 2. On creating the Fourier
transfol1.nation hologram of based patterns, a based pattenl set on lens L1 of the font focus point. Then, the Fourier
transfoll11ation hologram is lnade on the P2 plane by the reference bealn from b which set on the PI plane. Also, on the
cOITelation operating, the lnade holograln is set on theP2 plane. Then, the objective shift data is set on the front focus point.
We have tried to set it on the distance d froln the lens L 1.
Input plate Filter
PI P2
x a
-b 0'2
---
0'I
b 0'3
f
(9)
(10)
Fig.2 Optical correlation systenl
for tueasureing three ditnensional intoflllation.
Then, we think that we take the cOlTelation betweena complex a1l1plitude based pattelTI and an objective dataAn amplitude
transmission distribution T A ( a, 13 ) of the based Fourier transfonnation on the P2 plane is ;
{ 2}a [3 2TA{a,f3) = Se(1/' AI) + RAO
a [3 { . a}
+ SC(AI' 1/}· RAOexp 27gb 1/
* a [3 { a}+ seC1/, 1/}· RAOexp - 27ifb 1/
where * is complex conjugation, (a, (3 ) is the coordinates on the P2 plane, A. is the wavelength, f is the distance of
focus point, Se( a / A ~ (3 / A f) is the Fourier transformation of sc(x,y), RAois an alnplitude ofa reference beam on the
P2 plane. The b is x coordinates of the reference beam on creating the Fourier transformation hologram.
Therefore, the light intensity distribution E( a , 13 ) through the P2 plane is ;
E (a, [3) = GA(.!!-.,J!...) •T A(a ,[3)AI AI
= G{~':).{ sc(~,~) 2 + R~O}
+ GA(!!- J!_J •sc(.!!:.... L I. RAoexP{27ifb.!!:....}AI '1/) '}if , AI) }if
+ GA(!!-,LI. s~(.!!:....,LI. RAoexp{- 27ifb!!-}AI 1/) '1/ AI) 1/
where GA ( (¥ / A "( 13 / A f) is the Fourier transfonnation of gA(X,y).
(11)
(12)
(13)
(15)
(14)
10
Then" the mutual correlation image between an objective data and a based pattern is taken by the third tenn ofthe equation
(10). Therefore, we think about only third term of the equation (10).
(a 131 +(a 131 {. a}E3(a,f3) = GA y' y). Sc AI' AI)· RAOexp - 27gb Y
When the objective data is set on the PI plane which is the distance d fi:om lens L 1, the light intensity G' d( a , [3 ) on
P2 plane is;
G~(a,f3) = exp[jk(a22j2j(1_ ;)]- FT{gA (X,y)}
[.(a2 +f3 2i( d J] (a 13)= exp ] k 2I ) 1- I) • GA y' AI
where F T is Fourier transfonnation operator" and k = 2 TC / it .
R is the distance from the point" oforigin to objective plane. The based pattern as Sc,~=o is a complex amplitude distribution
at Z=O. This distribution is equal to the phase distribution which is the distance R from the point sources.Therefore, this
distribution S' c,z=o( a 'I 13 ) on P2 plane is;
S~.z=o(a,f3)= exp[jk( a22j2j(1_ R; I)]. FT{8(x,y)}
= exp[jk( a
2
212J(- ;)]
This equation is equal to Fourier tranSfOlTIlation S' c,;z=o( a / A ~ 13 / A f) of Sc,;z=o. This recorded distribution as the
based pattern is set on P2 plane. Then, on setting the observed datagA(x,y) at the distanced fromlensLl, the light intensity
E3( a" 13 ) is given by equation (10);
E 3 (a,f3) = G~ (a,f3)· {Sc.z=o(a, 13)r·RAoexp{ - 2njb ; }
= exp[jk(a 22j2J( R+(j -d))l GA(~' ~J
·RAoexp{ - 2~bt}
On setting the incident plane PI shown as Figure 3 (d=f), the first term of equation (14) is equal to a complex amplitude
distribution of the equation (13) as the equation (15). Therefore, the mutual correlation image as shown equation (15) is
given by correlation between the based pattell1 sc,;z=o(x"y) and the objective data gA(X,Y).
[ . (a
2
+f3
2i(RI] (a 131 [. a]E3.d=/ (a, 13) = exp]k 21) 7) ·GA AI' y)' RAOexp - 2n]b y
={Sc z-o(a ,f3)}* .GA (.!!...-,.1!.-) .RAo exp[- 2nj b.!!:-]
. - . AI AI Y
Also, on the case of setting the incident planePI shown as Figure 3 (d = f- a), the given distribution is equal to a complex
amplitude distribution at Z=a. Therefore, the mutual correlation image as shown equation (16) is given by correlation
between the based pattern Sc,~=a(X,y) and the objective data ~(x,y) .
E 3d-{ (a, 13) = eXP[ik(a2+ f32)(R + aI]. GA(.!:.-,J!.J ·RAoexp[- 2~b..!!:....]
· - 21 I) AI AI) AI
(16)
= {S~,z=a(a,f3)}' GA(~' ~) · RAoexp[- 2~b ~ ]
As mentioned above, we have taken the mutual correlation between the based pattern at Z coordinates and the objective
11
data by sifting the incident plane PI. The advantage of this Illcthod is the needless to change a based pattenl at each Z
coordinates.. that is to use only one based pattern (Z=O). So, this systeul is the high utility factor to cut down forlnakillg
a based pattern. Furthennore, this systeln is able to reduce a lot OftllelnolY for recording based patterns.Therefore, the depth
resolution is improved.
Input plate PI Filter P2 Output plate P3
Ll L2
k ~= f· a*-f->/<
I"d=f ~
~ d=t+a >I
f >/<-f->/
Fig.3 Slide of input plate Pl.
Sirl1ulntion
This section shows the silnulation as shown Figurc 2. We calculated by giving variatiollofthe valueofa. Figure 4 shows'
the object that is A(2.. 0..-5) .. 0(0.0.0).. B(-2,0.5).
\\'e used the objective data (512X512) which is Illade in the calculator. The only one based patten1 is the cOlnplex
alnplitude distribution at Z=O. The result shows in Figure 5. The l10rtllalized light intensity ofeach points is recognized
by the Inaxilnuln value of the con·clation result.
x
z .
D
-•.... ::.
Fig.4 Arrangemelit of point sources.
.~
co
d
en
c::
C1)
'0
.5 d
""tj
0
.~ ~
c:; d
E
0
Z Nd
. . .
..........r.···.·.·.·.·r.· '.;' :: ;.- J ·.1~.·.·.·.· .
-+- (-2.0)
--- (0. Q)
--.- (2. 0)
o
7..5 10 (mm).5-10 -7..5 -.5 -2..5 0 2..5
Z coordinates
Fig.5 The result of calculator simulation.
12
Optical simulation with complex amplitude pattel"n matching
This section shows an optical sitnulation to evaluate optical cOlTelation systeln.
The optical measuring system is as shown in Figure 6. We have used He-NeLaserand lensLI, L2 which focus on 25[em].
In the case ofmaking a based Foutier transfJnnation holograln, The point source ofthe re~rence is made by a pinhole
B(PH.B) and composed by a halftnirror (HM). The gap between the original point and the reference beam on PI plane is
made by moving a HM ~n parallel as shown in Figure 6.
MI
He-Ne Laser
LO PI Ll P2 L2 P3
Fig.6 Optical llleasuring systelll.
Thus, the incident plane P 1 is set with inputting directly the wave font ii'om the point source (PH.A) as the complex
amplitude distribution based pattelll. The point source is set the locate which is distance R from the P I plane. Then, the
wave tront of the point source reach the P 1 plane without lens LO. This wave tront is an object beam. The Fourier
transfolmation hologram of the bas~d pattenl is made by the reference beam of the pinhole (PH.B) and the object beam,
In the case ofoperate a cOlTelation, The Foutier transfonnation hologratn ofthe based pattern set on theP2 plane by cutting
the reference beam and the objective data set on the PI plane. Then, lensLO set to incident a parallel beamon thePI plane.
The result on P3 plane of a con'elation between the based pattenl each Z coordinates and the objective data onPI plane is
taken by sifting the P 1 plane. Then, the tlu'ee dinlensional infonnation of the object is taken by getting the light intensity
distribution with CCD calnera as shown in Table 1. Also, the pixcel pitch of the object image data shows in Table 2.
Table 1 Specification of CCD calnera.
CCDCAMERA
(XC-77 SONY)
Pixcel 768(H)X 493(V)
Area 8.8(mm)X6. 6(mm)
Translate Inter line lnethodlnethod
Cell size 11 (/L 111 ) X13 ({1 111 )
Chip size 10.0 ({1 111) ><8.2 (f-l 111)
Table 2 Specification of flame memory
horizontal 1.33XIO -(lnnl)
vertical -21.34X 10 (mIn)
We have used the object data which is used in the above calculator sinlulation as three point sourcesA(2,0,-5), 0(0,0,0)
and B(-2,0,5). Figure 7, 8 shows the result. Figure 7 shows the change ofthe light intensity distribution on (2,0), (0,0) and
(-2,0). The light intensity distribution is nonnalized by the tnaXilllum value of the given data. The pitch ofZ coordinates
is equal to the one ofsifting (in this case; 2.5[lllin]). On the Z coordinates which the point sources exist, the normalized light
intensity each Z coordinates take the maxillluln value. Figure 8 shows the intensity ofX coordinate. The light intensity
distribution is nonnalized by the maximuill value ofthe given data. The spread of the point at peak value is 16 pixcels
[0.21 mm].Therefore, we can detect the three dimensional infonnation by the above lnethods which is sifting the object data.
13
N
d
.......:........ • --+- (2. 0)
. . ' --- (0.0)~ ; ~ ~ : : ~ (-+- (-2. 0)
...... ······~·········:·······T·····T······r··· .
...... j ! / ( t" ! i .
o
-10 -7.5 -5 -2.5 0 2.5 oS 7.S 10 (mm)
Z coordinates
Fig.? The result of optical detection simulation (1).
y=O/ z=-5
.3.4(mm)2.00.0
x coordinates
-2.0
~'-- ---I"- --L- ...L.- _
-.3.4
.3.4(mm)2.00.0
x coordinates
-2.0
~'-- --I --L- ...L.- _
-.3.4
~
~-
~
~- A .I I.a
~ I I I
-.3.4 -2.0 0.'0 2.0 .3.4(mm)
x coordinates
Fig.S The result of optical detection simulation (2).
14
conclusion
In this paper, we propose the method that extracts three-dimensional information by sifting the plane of
observation phase inforlllation data with the improved optical correlation system.
We can collect based patterns to only one by shifting observation data plane with colllplex
alllplitude pattern matching. Then, the lllany 11lelllory becollle needless and the processing time is
shortened. Therefore, we can correct the weak point of the forIner 11lethod.
References.
1) M.E.Lucente, RPappu, C.J.SpalTell, and S.A.Benton, SPiE international Conference, 2577, 2 (1995)
2) Shirai, Chihara, and Shirae, Signal systenz control symposiunl, El, 69 (1990)
3) Ueda, Takahashi, and Shinlizu, TV, 48, 10,1230 (1994)
4) Sakata, Ichino, Takahashi ,and Shimizu, Denki,G15-6, G415 (1993)
5) Yabe, Ito, and Okazaki, Jpn.J.Appl. PhysPart 2,32, 9B, L1359 (1993)


Extracting Three-dimensional Information with Complex Amplitude : Pattern Matching using a Holographic Method

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Extracting Three-dimensional Information with Complex Amplitude : Pattern Matching using a Holographic Method

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