Hidden grids from the photocopy process are used to produce moiré patterns. The method of production of moiré patterns is extended to hidden grids generated in the optoelectronical CCD observations. An application of this moiré is proposed to measure distances.Facultad de Ciencias ExactasFacultad de Ingenierí

Garavaglia, Mario José

Laquidara, Anibal Pablo

English

El Servicio de Difusión de la Creación Intelectual

Hidden grids, moiré patterns and optoelectronically 
measurement of distances
Mario G arava oli a and AnibaJ Pablo Laquidara
Keywords; photocopier hidden grids, CCD hidden grids, moire effect, distance measurement.
1. H ID D E N  G R ID S  A N D  M O IR E  P A T T E R N S
Various methods exist to make photocopies o f  an original image. Photocopies are produced on opaque paper or transparent 
plastic sheets The original image can also be a slide that is projected onto the photocopier window or scanned. Each method 
has its proper form to generate the copied image. In general, matrix o f  equally or stochastically spaced points or equally 
spaced lines are employed to reproduce half tones and colours. Figure 1 show's these two types o f  hidden grids observed 
under microscope. Also, Figure 1 shows the Fraunhofer diffraction patterns o f  both grids. The light sources used were a 15 
cm  k>sg filament lamp and a fluorescent tube.
The matrix of points of the array o f  lines can be considered as hidden grids that are incorporated to the image through the 
pkrtocopy process. Hidden grids can be used to encode information into the reproduced image in order to characterize some
properties o f  the original object.
This paper deals vrith an application o f  the hidden grids to measure distances in the original object space using the moiré 
effect to decode the necessary information.
2. P R O P O SE D  M E T H O D  T O  M E A S U R E  D IST A N C E S  
Figure 2 show's the geometrical optics principle to form an image through a lens. Let be the object a plane -like a wall- that 
is perpendicular to the optical axis o f  the photographic objective O. The optical axis corresponds to the Z axis o f the 
Cartesian reference system (X, Y, Z). Onto the photographic film, the coordinate system (x, y, z) is the Cartesian reference 
in the image space. The optical axis corresponds to the z axis. Points Pj and P2 on the wall are reference marks to define 
the metric in the object space. They are separated a distance D. Points pt and p2 are the images o f  Pt and P2 , which are 
reproduced without aberrations. If the distance L from the camera objective to the wall is large enough, the distance d from 
point p3 to point on the film can be expressed as d  f  D/L, where f  is the focal lenght o f  the objective. If the 
photographic camera is rotated an angle a  around the z Z axis, the distance d maintains its value on the film because it is an 
invariant under rotations.
The proposed method to measure distances requires o f  two slide pictures o f  the wall to be photographed. The first one 
corresponds to the position o f  the camera on which x-axis and y-axis on the film are parallel to the X-axis and Y-axis on the 
wall respectively. The second slide picture corresponds to the position o f the camera rotated an angle a  around the z Z axis. 
Transparencies from both slides are prepared in the normal fashion. Each transparency reproduces an enlarged slide image. 
Points p: and p2 on the slides are reproduced as points pj and p 2 on the transparencies. I f  the magnification o f  the 
photocopier optical system is M, the distance d between points p \  and p 2 can be expressed as d  Md. Besides, the 
superposition of both transparencies generates a moiré pattern. In order to measure distances the superposition must be done 
is such a wav that images of p i and p and p 2 and p ^  be in coincidence. Then, it is possible to observe moiré fringes 
gesseraied by transparency hidden grids rotated through an angle a . So, it means that the moiré pattern decodes the rotation 
operation risai was encoded in transparencies. Figure 3 describes the geometrical situation. If the period o f  the hidden grid is 
T$, ite  period of the observed moiré fringes results:
348
Departamento de Física, Facultad de Ciencias Exactas y Departamento de Electrónica, Facultad de 
ingeniería. Universidad Nacional de La Plata (UNLP), and Centro de Investigaciones Opticas 
(CONICET CIC), La Plata, Argentina, Tel/Fax + (54)(221) 471 4341, E-mail: 1 aserlab@pinos.com 
and garavagliam@ciop. unlp.edn. ar
ABSTRACT
Hidden grids from the photocopy process are used to produce moiré patterns. The method o f production o f  moiré patterns is 
extended to hidden grids generated in the optoelectronical CCD observations. An application o f  this moiré is proposed to
measure distances.
-
-
-
=
-
-
= 
-
length, shape and position measurement 1.89
Figure 1. a) Hidden matrix 100 jim x 100 pm point array (Kodak color thermal copier); b) Hidden grid 128 pm spaced lines 
(Cannon color laser copier); c) Fraunhofer diffraction pattern o f the hidden array at a) using a 15 cm long filament lamp as 
light source (positive), and d) Fraunhofer diffraction pattern o f  the hidden grid at b) using a fluorescent tube as light source 
(negative).
Figure 2, The photographic objective PO forms images pi and p2 onto the film surface from points Pj and P2 placed onto 
the wall surface.
Then, the distance d  can be expressed as a function o f  T. The bisector BB o f hidden grids is perpendicular to moiré 
fringes. As the segment d' forms an angle p with B B , it is possible to express d  as a function o f  T. Taking into account 
that the positions o f points p'v  p'ia and p'2 a  p'2a can be placed between moiré fringes, it is necessary to introduce the 
fractional orders ei and e2 o f  a period in the moiré pattern, as it is shown in Figure 3. Finally, the distance L from the 
photographic objective to the wall, can be expressed as:
3 4 9
' ' 
' '
= ' 
1 .9 0 module 1
Where n is the number o f  compiete moiré periods contained in d' cos 3.
An easy observation o f  the moiré pattern can be achieved through the Fraunhoffer diffraction pattern o f hidden grids. Figure 
4 shows the moiré pattern superimposed on the diffraction pattern.
Figure 3 The moiré field positions o f  the ends o f  the segment d  corresponding to points p'i  p ]a and p 2 «  p 2<x are 
defined by the fractional orders s } and e2 with respect to their neighbour left moiré fringes.
Figure 4. The moiré pattern superimposed on the diffraction patent
350
' = ' ' ' 
length, shape and position measurement 1.91
Figure 5. Water tank o f  the Campus of Technology at Gonnet photographed from 200 m. a) horizontal view and b) inclined 
view. Note the three white reference marks on tank columns.
Figure 6, CCD detector microphotograph. Pixels are 8.8 pm x 8.8 pm area.
Figure 7. Water tank at Figure 5) captured from 50 m. by the CCD camera and enlarged 8:1 on the screen monitor, a) 
horizontal view and b) inclined view. Note the pixeled pattern o f the image and the three white reference marks.
3 5 1
1.92 module 1
3. CONCLUSION REMARKS AND PROPOSALS
A method to measure distances can be accomplished by using the moiré pattern generated by transparency-hidden grids. 
However, these types of grids are physically unstable because they suffer the thermal copying processes. More stable and 
closed grids are observed in CCD optoelectronically captured images. Then, the pure optical method to measure distances 
can be extended and converted in a pure electronical one. Figure 5 shows a typical view o f the CIC  Campus of 
Technology at Gonnet. Both pictures -Figure 5 a) and b)- were photographed from a distance o f 200 m; they were pictured 
by rotating the camera through the optical z Z axis an angle o f 7.5°. The same pictures al Figure 5 were captured using a 
CCD camera, whose detector was microscopically observed. Figure 6 shows an enlarged view o f a part o f the CCD 
detector. The area o f  each pixel is 8.8 pm x 8.8 pm. The pixel area o f  the CCD camera generates an optoelectronical hidden 
grid. Finally, Figure 7 a) and b) show screen monitor pictures o f the campus water tank basis; 8:1 zoom was applied and the 
pixeled structure o f the CCD camera is easily observed.
Figure 8 shows the electronically generated moiré pattern between the information contained in figures 7 a) and 7 b).
A scale scene was defined by three reference marks using three white targets pasted on the concrete columns o f the water 
tank. Following the described moiré procedure between both optoelectronical grids, distances o f the order o f hundred meters 
were measured with an uncertainty o f 2%.
4. ACKNOWLEDGEMENTS
This work was partially financed by CONICET (PID-BID-CONICET 1116/91 grant) and UNLP (FCE-3711/97)
5. REFERENCE
1. Hidden grids, moiré patterns and measurement o f  distances.
Mario Garavaglia
III Reunión Iberoamericana de Optica (III RIAO) y VI Reunión Latinoamericana de Optica, Láseres y Aplicaciones 
(OPTELAS 98), 28 de setiembre a 2 de octubre de 1998, Cartagena de Indias, Colombia, Poster 133.
2. Electronic CD edition by Academia Colombiana de Ciencias Exactas, Físicas y Naturales. ISBN 958-9205-32-1
352
Figure 8.Moiré pattern generated by the electronical superposition o f Figures 5 a) and b).
-
-
’ 


Hidden grids, moiré patterns and optoelectronically measurement of distances

http://sedici.unlp.edu.ar/bitstream/handle/10915/80396/Documento_completo.pdf?sequence=1

Hidden grids, moiré patterns and optoelectronically measurement of distances

Abstract

Similar works

Full text

Available Versions

El Servicio de Difusión de la Creación Intelectual