116
tion to the contouring problem. The brief de-
scriptions of the various methods are in-
cluded only to provide continuity.
MOIRE CONTOURING
Moire techniques of generating elevation
contours on opaque objects had been dem-
onstrated over a decade ago.!.3. In its
simplest form it consists of an amplitude grat-
ing such as a Ronchi ruling placed close to the
object, as shown in Figure 1. The combina-
tion is illuminated by a quasi-point source at
an angle 6 to the normal ofthe grating surface.
The observation is made along the normal
direction. The moiré pattern between the
projected shadow on the object and the grat-
ing represents an instantaneous display of
elevation contours. The contour interval has a
value given by dh = d/ tan0 where d repre-
sents the period of the grating.
During the past several years several mod-
ifications to this basic method have been
proposed and demonstrated. Some of the sig-
nificant and modifications are listed in this
paper, and the reader is referred to the refer-
ences for additional information. The con-
trast ofthe moiré fringes obtained by the sim-
ple system described above greatly depends
on the contrast of the grating and the pro-
jected shadow, the distance between the ob-
ject surface and the grating, and the nature of
the illumination*. One ofthe simplest of ways
to improve all these parameters is by forming
the shadows on the object through a projec-
tion system. The shadows on the object can
be formed by either projecting the image of a
Ronchi ruling on the object or by interfering
two coherent plane waves on the object. The
DIRECTION OF
OBSERVATION
"€.
“> ILLUMINATION
rn ET GRATING
(C RN e
Fic. l. Moiré contouring.
PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING, 1976
shadow on the object in turn is imaged on to
another Ronchi grating and the resulting
moiré fringes once again represent elevation
contours.
The carrier frequency patterns due to the
grating and the shadow often interfere with
the observation of the contour fringes by in-
troducing noise terms. This can be avoided
by first recording the shadow pattern on the
object and then processing the record sub-
sequently using an optical system shown in
Figure 2. The interfering plane waves behind
the record provide the demodulating refer-
ence pattern. The contour fringes, which rep-
resent low spatial frequency information, are
spatially filtered using the low pass filter
from other noise terms.
As stated earlier the contour interval is
equal to the period of the projected shadow
pattern when the angle of projection is 45*.
Hence the resolution ofthe moiré contouring
method depends on the spatial frequency of
the projected shadow. For increased resolu-
tion, the projection and the imaging systems
must be low f-number systems. This automat-
ically limits the elevation range since, as the
f-number ofthe optical system is lowered, the
depth-of-focus becomes reduced drastically.
This limitation can be overcome by modify-
ing the manner of processing the photo-
graphic record. In this scheme a fringe pat-
tern is projected on the surface under test by
two coherent plane waves inclined at an
angle $. The projected pattern is then re-
corded on a photographic plate placed at the
image plane of a recording lens. If 0 is the
projection angle, the intensity distribution on
the object can be written as
I(x,y) =1 + cos gr + h(x) tan0) (1)
where d is the fringe spacing given by
d = Mcose, À being the wave length of illu-
minating radiation. The amplitude transmis-
sion ofthe photographic record is then given by
t(x,y) =k(1 + cos 2 (x + h(x) tang) (2)
where k is a constant of proportionality. The
photographic plate is then bleached to con-
vert the amplitude transparency to a phase
transparency. The amplitude transmittence
of the plate is now given by
t(x,y) = exp i(a, cos es (x h(x) tan89)) (3)
where a, is a constant representing the
amplitude of phase relief. Equation 3 can be
written as
