TECHNICAL FIELD
[0001] This invention relates to acoustooptic light deflection apparatus. More particularly
it relates to apparatus for deflecting two or more beams of light of different wavelength
through substantially the same scan angle.
BACKGROUND ART
[0002] It is well known that the passage of acoustic waves through a transparent medium
produces a diffraction grating by periodic variation of the index of refraction of
the medium. Light directed through the medium, or cell, is diffracted through a diffraction
angle a, between the undiffracted and diffracted beams, according to the following
formula:
for small values of a and where.1 is the vacuum wave length of the light, f is the
frequency of the acoustic wave, and v is the acoustic velocity. In acoustooptic deflectors,
light is deflected or scanned through a scan angle Δα by varying the acoustic frequency
f.
[0003] However, it can be seen that equation (1) defines a different angle a for each wavelength
subjected to the same'acoustic wave. If frequency f is continuously varied through
a bandwidth Δf, light beams of different wavelength will scan through different scan
angles according to
[0004] These characteristics are illustrated in Fig. 1. A conventional diffraction cell
10 contains acoustic waves 12 of frequency f
_{l} produced by a transducer 14, which is in turn energized by a signal source 16. Two
beams of light having wavelengths λ
_{1} and λ
_{2} where λ
_{1}<λ
_{2} travel along a path 18, enter the cell 10 and are diffracted by the acoustic wavefronts.
Since the angle of diffraction is a function of optical wavelength, the light of each
wavelength exits at different respective diffraction angles a
_{1} and a
_{2}.
[0005] If the frequency of acoustic waves 12 is changed from f
_{1} to a higher frequency f
_{22} the diffraction angles will change in accordance with equation (2) by Δα
_{1} Δα
_{2}, respectively, where Δα
_{1}<Δα
_{2}. Thus, it is apparent that, even if the diffraction paths of the two wavelengths
could be made co-linear at one chosen frequency,such as, for example, by impinging
beams of different wavelengths at different respective incident light angles, they
would not remain co-linear as the frequency is varied.
[0006] In their article "Equalization of Acoustooptic Deflection Cells in a Laser Color
TV System", Applied Optics, Vol. 9, No. 5, May 1970, W. H. Watson and A. Korpel suggest
the use of an acoustooptic deflector in a three color laser television apparatus.
They recognize that the dispersive characteristics of acoustooptic deflection require
some form of electrical or optical compensation before three primary color images
will remain in register as the acoustic frequency is varied over a bandwidth Δ f.
Electrical compensation requires. different acoustic signals for each beam, thereby
apparently requiring a separate acoustooptic cell for each beam. Watson and Korpel
optically equalize the scan angles using separate compensating prisms to magnify the
smaller blue and green scan angles to match the scan angle of the red beam.
[0007] The optical solution suggested by Watson and Korpel requires different prisms for
different beams. This requires spatially separate beams. Watson and Korpel provide
spatially separate beams by using three separate acoustooptic deflectors driven by
the same signal.
DISCLOSURE OF THE INVENTION
[0008] It is the object of the invention to equalize the scan angles of two or more acoustooptically
deflected beams using an optical means without the need of spatially separating the
beams prior to the optical means. With this invention a single acoustooptic deflector
can be used to deflect two or more beams while the prior art uses separate deflectors
for each beam.
[0009] This object is accomplished by provision of prism means positioned in the path of
both beams which prism means magnifies the scan angles of both beams by an amount
which is an inverse function of the wavelengths of the beams.
[0010] According to a preferred embodiment of the invention, a single prism having indexes
of refraction n
_{1} and n
_{2} for the wavelengths in question and an apex angle A is positioned with the deflected
light beams incident on its frant surface at approximately the same incident angle
θ. The parameters n
_{1}, n
_{2}, A and θ are chosen so that the product of the wavelength and the magnification of
scan angle of one beam is equal to that of the other beam.
[0011] According to a further preferred embodiment a single prism is used to equalize the
scan angles for three light beams of different wavelength, by proper choice of n
_{1}, n
_{2}, n
_{3}, A and θ.
[0012] Even if the light beams are eventually separated, for example, to insert other optical
elements to equalize the diffraction angles, it is an advantage of the invention that
the prism means provides such separation or greatly shortens the optical path necessary
for such separation. Therefore, according to another embodiment, three beams of different
wavelength are passed through a single prism which equalizes the scan angle of two
of the beams and contributes to the separation of the third beam from the first two.
The scan angle of the third beam is equalized with the first two by further magnifying
its scan angle with a second prism positioned only in the third beam.
BRIEF DESCRIPTION OF THE DRAWINGS
[0013] In the description of the embodiments of the invention presented below, reference
is made to the accompanying drawings in which:
Fig. 1 is a schematic representation first referred to above,of two light beams of
different wavelength passing through a diffraction cell, with greatly exaggerated
scan and diffraction angles;
Fig. 2 is a schematic view of an optical achromatization system according to the invention,
with greatly exaggerated scan and diffraction angles;
Fig. 3 is a plot of light deviation of a prism vs.. incident angle;
Fig. 4 is a plot of scan angle magnification of a prism vs. prism apex angle;
Fig. 5_{' }is a plot of scan angle magnification of a prism vs. incident angle;
Fig. 6 is a plot of the magnification ratios of a prism for two optical wavelengths
vs.incident angle; and
Fig. 7 is a schematic view of an optical achromatization system according to another
embodiment of the invention, with greatly exaggerated scan and diffraction angles.
DETAILED DESCRIPTION OF EMBODIMENTS
[0014] Acoustooptic deflectors normally function at very small scan and diffraction angles,
for example, less than 1
^{0} in each case. However, these angles are shown much greater than this in the drawings
for illustrative purposes.
[0015] Referring to Fig. 2, a schematic representation of light deflector apparatus, constructed
in accordance with the present invention, is shown. Diffraction cell 10 is identical
to that shown in Fig. 1, described above. As in
_{F}ig. l,the acan angles of beams exiting from cell 10 vary in direct proportion with
wavelength. The apparatus is optically achromatized by prism means, for example, single
prism 26 positioned in the path of the deflected beams to differentially magnify and
thus equalize the scan angles of the different wavelength light. A pair of centering
mirrors 26 and 30 realign the beams so that all rays impinging upon an imaging lens
31 at any instant are parallel. The lens focuses the parallel beams to a point at
plane 32, which point varies according to the scan angle.
[0016] The parameters of prism 26 are selected in accordance with the present invention
so that -the scan angle A a of each beam is magnified by an amount necessary to equalize
the scan angles of the two beams. In the following sections of this specification,
we will discuss those parameters which affect scan angle magnification and how such
parameters are used to achromatize the beams.
[0017] Because the prism means is placed in the path of both beams, it is not necessary
to spatially separate the beams prior to entering the prism as in the prior art. However,
an advantage of the invention is that the prism greatly shortens the path required
to separate the beams for optical elements such as centering mirrors 28 and 30. In
fact, if the scan angles of the original diffracted beams overlap and emanate from
the same point in cell 10, they will never separate without the prism or other optical
elements.
Scan Angle Magnification
[0018] The angle between the path of the incident and emergent rays of a light beam passing
through a prism is the angle of deviation D. The amount of deviation is dependent
upon the index-of refraction n of the prism material for the particular wavelength,
the apex angle A of the prism and the incident angle θ (the angle between the incident
light beam and the normal to the incident prism face). The relationship between these
parameters is:
[0019] 'From equation (3), it is seen that, for a given prism and wavelength, deviation
of a light beam is a function solely of the incident angle θ. Fig. 3 is a typical
plot for two different optical wavelengths λ
_{1} and λ
_{2} of deviation versus incident angle. Note that as the angle of incidence is, say,
decreased from a large value (moving from right to left), the angle of deviation decreases
at first and then increases. The angle of minimum deviation D
_{m} is related to the apex angle of the prism and its index of refraction as discussed
in Sears and Zemansky, University Physics, 2nd Edition, Addison-Wesley Publishing
Company, page 736.
[0020] The magnification M of the prism at any value of incident angle θ is equal to the
slope dD/dθ.
[0021] Of course, the change in incident angle Δθ of a beam arriving at a prism face from
an acoustooptic deflector cell as in Fig. 2 is linearly related to the change Δain
the diffraction angle a of the cell. From equation (2), the scan angles Δα
_{1}, Δα
_{2},...,Δα
_{n} corresponding to light of wavelengths λ1, λ2, ... λ
_{n} are directly proportional to wavelengths. Mathematically, such a relationship can
be expressed as follows:
[0022] Accordingly, if the scan angles Δα
_{1} (where i is any integer are multiplied by a factor M
_{1} which is constant over the scan angle Δα
_{1} and inversely proportional to the associated optical wavelength, the resulting scan
angles would all be the same. Another way to express the same relationship is:
where
[0023] From this relationship and from Fig. 3 it can be deduced that a prism is one device
wherein magnification varies inversely with wavelength. That is, the prism magnification
M cam be greater for shorter optical wavelengths. In the region to the left of the
point of minimum deviation in Fig. 3, the slope for the shorter wavelength λ
_{1} -s more negative than that for the longer wavelength λ
_{2}. Unfortunately, the relationship is not linear. However, if specific values for the
parameters can be found where the relationship holds for two or more specific wavelengths,
very close achromatization over small diffraction and scan angles can be effected.
Selection of Apex Angle
[0024] Deviation as a function of the apex angle can be computed from equation (3) for a
given prism material and a fixed incident angle θ. In fig. 4, magnification (dD/dθ)
is plotted against apex angle for red and blue light beams (respective wavelengths
of 6328A and 4416A) at an incident angle of 35°; using a prism having an index of
refraction N
_{D}= 1.68893 and a dispersive index v
_{D=} 31.08.
[0025] For large apex angles, the absolute magnitude of the scan angle magnification increases
as wavelength decreases, a desirable effect to compensate for the differences in scan
angles Δα
_{1} from acoustooptic cell 10. Thus, in order to obtain prism magnifications that are
an inverse function of a wide range of optical wavelengths, we must choose relatively
large prism apex angles.
[0026] However, as the apex angle gets larger, the critical angle will eventually be reached
for the blue beam. Therefore, the chosen apex angle cannot be so large that any light
beam will suffer total internal reflection within the prism.
Incidence Angle for Two Color Scan Equalization
[0027] Once a prism apex angle is chosen, the relative magnification can be adjusted to
the desired value by choosing the appropriate angle of incidence 0. Acoustooptic deflectors
commonly function at very small scan and diffraction angles. For example, both angles
may be less than 1°. For this reason, a single angle θ is used for all wavelengths
in determining.prism parameters and orientation. If the angle θ varies substantially
between beams, then allowance for such variance must be made, which allowance is within
the skill of the art.
[0028] Fig. 5 shows a pair of plots of magnification versus incident angle for a 40° apex
angle prism having indexes of refraction n
_{1} and n
_{2} of 2.08537 and 2.16790 for red (λ
_{1} = 6328A) and blue (λ
_{2} = 4416A) respectively. It can be shown that at θ = 32°, M = constant /λ for the red
(6328 A) and blue (4416 A) lines for such a prism. Thus, there is an incident angle
at which the magnification will be inversely proportional to the optical wavelengths
6328 A and 4416 A for that particular prism.
[0029] In determining the incident angle at which the desired relationship between magnification
and wavelength exists, we define Rij ≡ M
_{i}/M
_{j}, where i and j are integers. If only two colors λ
_{1} and λ
_{2} are to be deflected, achromatization will be achieved where M
_{1}λ
_{1} = M
_{2} λ
_{2}, or
^{R}_{12} = λ
_{2}/λ
_{1}.
[0030] Consider the three wavelengths λ
_{1} = 6328 A, λ
_{2} = 4416 A, λ
_{3} = 5210 A. For the pair λ
_{1} and λ
_{2}, or the Fair λ
_{3} and λ
_{2}, respectively we require that:
and
[0031] In Figure 6, computed magnification ratios
or R
_{ij}, are plotted vs. prism incident angle θ for a prism of the same glass as in Fig.
5 (n
_{3} = 2.11493) with 30° apex angle for the three optical wavelengths λ
_{1} = 6328 A, λ2 = 4416 A and λ
_{3} = 5210 A. The circled points indicate those incidence angles at which the condition
of either equation (6) or (7) is fulfilled, i.e., where R
_{ij} = λ
_{j}/λ
_{i} (R
_{12} = 0.6979and R
_{32} = 0.8476). Thus, if-one uses this prism at an incident angle of 29.6°, scan equalization
is achieved for the two colors λ
_{2} = 4416 A and λ
_{1} = 6328 A. Similarly, achromatization of the scans of the two colors λ
_{3} = 5210 A and λ
_{2} = 4416 A is achieved by choosing θ = 28.0°. Of course, as the deflection angle a
varies over a range Δα, the incidence angle 0 will vary over a corresponding rangeΔθ,
and optimum performance will result if the change in R
_{ij} in Fig.- 6 is as small as possible over the range Δθ. Two color achromatization holds
over a larger scan range A a in the case of the upper curve since the slope of that
curve at θ = 28.0° is smaller than the slope of the lower curve at θ = 29.6°. Perfect
two color achromatization over the entire scan range requires that the change of R
_{ij} be zero over the range of values Δθ corresponding to the scan range of Aa.
Three Color Achromatization By Choice of Wavelengths
[0032] If the two circled points in Figure 6 were vertically aligned, i.e., if both equations
(6) and (7) were satisfied at a single θ value, then at that value of θ, M
_{i} = constant/λ
_{i}, or
[0033] There are several ways this can be done. One way consists of choosing the third wavelength
λ
_{3} to fit the achromatization conditions of the other two wavelengths. For example,
when equation (6) is satisfied, R
_{12} = 0.6979 for λ2 = 4416 A and λ
_{1} = 6328 A, and from Fig. 6, this is true. at θ = 29.6°. However, for the θ value 29.6°,
^{R}_{32} ^{=} 0.8050 and does not satisfy equation (7) with λ
_{2} = 5210 A.
[0034] We can use equation (7.) to find a value for λ
_{3} at θ = 29.6°. Letting R
_{32} = 0.8050 and λ
_{2} = 4416 Å, equation (7) can be solved for λ
_{3}; and we have λ
_{3} = λ
_{2} R
_{32} = 5486 A. Thus, if R
_{32} did not change with the change in λ
_{3}, simply changing from λ
_{3} = 5210 A to λ
_{3 =} 5486 A would accomplish three color achromatization. Of course, changing λ
_{3} does make a slight shift in.the upper curve of Fig. 6 and thus an iterative process
of solving for λ
_{3'} plotting R
_{32}, solving for a new λ
_{3}, etc., must be followed to approximate the correct value of λ
_{3}.
Three Color Achromatization By a Trimming Prism
[0035] Another technique, which does not require changing the wavelength of any beam, is
shown in Fig. 7.
_{'}A second "trimming" prism 34 has been used to compensate for the horizontal distance
between the circled points in Figure 6 by providing an additional control on the magnification
for one wavelength. Essentially, this involves separating one of the three beams for
individual magnification. A prism operating near normal incidence (θ = 0) has a magnification
M
_{o} given by
Solving for apex angle A,
[0036] Calculating as an example the value of A for a correcting prism needed in the example
of Figure 6, we remember that at θ = 29.6° (the incident angle θ which provides scan
equalization for wavelengths λ
_{1} 6328 A and λ
_{2}= 4416 A), the magnification ratio R
_{32} must be 0.8050 to equalize the scan of a third wavelength λ
_{3}. For two color scan equalization with λ
_{3} = 5210 A and λ
_{2} = 44l6A it has been shown that R
_{32} must equal 0.8476.
[0037] Hence, we see that we can have three color scan equalization without changing the
optical wavelengths (as was required by the technique of the preceding section) at
θ = 29.6° if R
_{32} is increased from 0.8050 to 0.8476. In doing so, M
_{2} cannot change because a change in the magnification of the λ
_{2} wavelength light scan angle would effect R
_{12} also. Therefore, only M
_{3} may be adjusted. The amount of adjustment in our example is determined by multiplying
the magnification ratio 0.8u50 by a factor which would bring it to 0.8476, or by 1.053.
This can be accomplished by magnifying the scan angle of the λ
_{3} beam by 1.053 by placing a "trimming" prism of magnification M
_{o}= 1.053 in the path of that beam.
[0038] If the same glass is used for both prisms'26 and 34 then
[0039] Thus, a trimming prism of apex angle equal to 9.5° in the path of the λ
_{3} beam would provide correct additional magnification of one wavelength.
[0040] This example illustrates an advantage of the invention. Prism 26 both equalizes the
scan angles of λ
_{1} and λ
_{2} and shortens greatly the optical path required before the beans separate enough to
use prism 34.
[0041] The invention has been described in detail with particular reference to certain preferred
embodiments thereof, but it will be understood that variations and modifications can
be effected within the spirit and scope of the invention. For example, additional
degrees of freedom can be obtained in matching three wavelength light with the desired
prism parameters if the prism is compound, for example, with two prisms of differing
dispersive characteristics either cemented together or airspaced.
INDUSTRIAL APPLICATION
[0042] The invention can be used in applications requiring scanning multi-color light. It
is particularly usable with discrete wavelength beams of small bandwidth such as those
produced by lasers. Accordingly, it can be used in laser color television receivers,
laser color printers and laser color copiers.