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by Michael Tidwell
Light Sources and Modulation (7.3)
Fiber Coupling (7.4)
Gaussian Beam Propagation (7.5)
Scanning (7.6)
Viewing Optics (7.7)
Appendix A supplements the material in this chapter. Appendix A contains photographs of the fiber coupling scheme, the Mechanical Resonant Scanner, and the see-through viewing optics (see Figures A1-A6).
The modulation scheme for the blue and green sources is acousto-optical (A-O) modulation. The video electronics amplitude modulates a 260 [MHz] carrier frequency generated by the A-O modulator sub-electronics (not shown in Fig 7.2.). The intensity modulated red, green, and blue light beams are then coupled into a single mode fiber of core diameter 3.1 [mm]. Fiber focusing optics focus the light exiting the fiber. The
tri-color beam enters the scanner assembly. The scanner assembly deviates the beam through a total angle of 25 [deg.] at a rate of 15.75 [kHz] in the horizontal direction and 18.75 [deg.] at a rate of 60 [Hz] in the vertical direction. The viewing optics collimate the tri-color beam, magnify the scan angle by a factor of 1.6, and present the video image to the eye.
The green light source was a Uniphase model 1676 green Helium-Neon (HeNe) laser of wavelength 543.5 [nm]. The maximum optical power of this device is 1.5 [mW].
Blue light is generated at 488 [nm] by an air cooled argon laser. The laser was purchased from MWK Industries and is believed to be an Omnichrome model 532 but the identity of the manufacturer was not guaranteed because the laser was purchased "used". The cavity of the laser contains a UV filter so as to protect the viewer from any unnecessary UV light entering the eye. The maximum power output of the argon laser is 14.5 [mW].
The successive horizontal lines in Figure 7.2 represent the modulated acoustic wave and the corresponding regions of refractive index variation [4]. The rise and fall time of the modulation in an A-O modulator is roughly [48]:
where D = optical beam diameter in the acousto-optic crystal, Va = the acoustic velocity in the medium, and te = the rise time of the RF drive electronics for the A-O modulators.
The beam diameter D in the A-O modulator is taken here to be the diffraction limited spot formed by the focusing lens,
where the wavelength is 534.5 [nm] for the green HeNe laser, the focal length of the focusing lens is 40 [mm], and radius of the limiting aperture is 0.4 [mm] and corresponds to the radius of the initial laser beam. The A-O modulator material is "fast" crystalline TeO2 (tellurium dioxide). The velocity of sound in "fast" TeO2 is
4.2 [km/sec] at 260 [MHz] [48]. The A-O modulators used for this project have:
where te = 3 [ns] for the A-O modulators in this project. A rise time of 10.8 [ns] is a best case scenario. In all likelihood aberrations in the focusing lens and misalignment will cause the beam diameter in the acousto-optic material to be larger and consequently to lengthen the rise time.
For the A-O device to be of any use the diffracted orders must be separable. Otherwise, the modulated and unmodulated orders mix. Gaussian beam theory states the smaller a Gaussian beam is focused, the greater the beam divergence (after the focused spot). If the optical beam is focused to a very small spot (to decrease the rise time of the modulator), the beam divergence is likely to cause overlap of the diffracted orders in space.
To correct this overlap, a higher carrier frequency is required. The higher carrier frequency, or frequency of the sound, creates a closer spacing in the diffraction grating generated by the sound column. The closer spacing in the diffraction grating causes greater separation of the diffracted orders. For this design an A-O modulator with a carrier frequency of 260 [MHz] was selected. The angular separation of the undiffracted and first diffracted order, 2qB, where qB is the Bragg angle is [4]:
where L = wavelength of sound in the material, and l = wavelength of light in the material. For the A-O modulator in this project,
Correspondingly, the angular separations of the orders for the green and blue channels are:
Lenses lg1, lg2, lb1, and lb2 are focusing and collimation lenses for the A-O modulators on the green and blue channels respectively. Lens lr1 is the corrective optic (for collimation) mounted on the laser diode and lens lw1 is the focusing optic for coupling the combined red, green, and blue channels into the optical fiber.
7.4.2 Cutoff and Normalized Frequency in a Step Index Single Mode Fiber
A parameter called the normalized frequency, V, determines the cutoff condition for single mode operation in single mode fibers [4]. For a step index fiber,
where a = core radius, n1 = core refractive index, n2 = cladding refractive index,
and l = freespace wavelength of the light. The cutoff condition in a step index fiber for single mode operation requires,
The wavelength corresponding to cutoff, lC , can be found by setting V = 2.405 and solving for l:
where,
and is the numerical aperture of the fiber. For the fiber used in this project,
and
lC is the shortest wavelength which the fiber can carry and remain single moded. The wavelengths in this project are all longer than the cutoff wavelength and the fiber can be assumed to be single moded for all colors in the display.
The mode spot radius, wo, can be calculated as the Gaussian equivalent beam radius that best approximates the LP01 mode profile [43]:
Table VII.1 shows the values of V and wo for the wavelengths and fiber used in this display.
For the values in Table VII.1, more than 97% of the power from coupling on the green and blue channels will be launched into the LP01 mode [42]. The mode launching distribution from the red diode laser is more complicated and not discussed here.
The propagation characteristics of an unguided Gaussian beam are presented here because Guassian beams do not follow geometrical optical rules and any analysis of Guassian beams should include diffraction considerations from the outset [2].
A Gaussian beam behaves, qualitatively, as shown in Figure 7.4.
Figure 7.4 shows the beam waist diameter d0, the angular divergence q, and the beam diameter as a function of the distance z away from the beam waist. Under geometrical rules, a beam converging at an angle q should eventually converge to a point [2]. Diffraction, however, does not allow this to happen. The beam waist diameter is a function of the divergence q and the wavelength l of the light:
Near the beam waist, the beam profile has a parabolic form such that
Rewriting gives
A distance called the Rayleigh range determines the extent over which one should take into account diffraction considerations for a Gaussian beam. Outside the Rayleigh range, wavefronts of the beam approach geometrical limits. The Rayleigh range is defined as the value of z where d = (2)1/2d0. This value of z is
The thin lens equation for Gaussian beams leads to predictions of beam waist size and location for paraxial lenses. If necessary, more detailed analysis can be done with ray trace software on a computer if coupling efficiency is insufficient. The Newtonian form thin lens equation for Guassian beams is
where z = the distance from the front focal point of the lens to the initial beam waist diameter do , z = the distance from the back focal point of the lens to the new beam waist diameter d0, and
or alternatively
and is added for diffraction effects [2]. The distance z is positive if the initial beam waist is outside (to the left of) the front focal point of the lens and negative if the reverse is true. The distance z is positive if the new beam waist is outside (to the right of) the back focal point of the lens and negative if the reverse is true.
It can be shown [2] that the new beam waist diameter is written in terms of the initial beam waist as:
where
Once a is calculated from known quantities, the new beam waist diameter, new divergence, and new Rayleigh range can easily be evaluated:
Clearly a shorter focal length focusing optic will produce smaller new beam waist diameter. A shorter focal length optic will also, however, be less forgiving in terms of angular misalignment as any angular difference in the incoming beams will be angularly magnified.
The version of the MRS used for this project is tuned to 15.75[kHz] with a mechanical deflection of 3.125 [deg.]. The vertical scanner is a Cambridge Technologies model 6800 galvanometer mirror operated at a mechanical deflection of 4.7 [deg.]. The galvanometer deflection can be selected according to the aspect ratio of the display and a ratio of 4:3 was chosen for this design. The galvanometer frequency is controlled by the video electronics to match the 60 [Hz] video frame rate.
The galvanometer and horizontal scanner are arranged in what is believed to be a novel configuration such that the horizontal scan is multiplied [45]. The scanners are arranged, as shown in Figures 7.6 and 7.7., such that the beam entering the scanner assembly first strikes the horizontal scanner then strikes the vertical scanner. The beam is reflected by the vertical scanner back to the horizontal scanner before exiting the scanner assembly. The beam therefore strikes the horizontal scanner twice before exiting the scanner configuration. In such an arrangement, the first scan (corresponding to the first bounce or reflection) is doubled by the second scan (corresponding to the second bounce or reflection). The case shown is for q = 45 [deg.] wherein the exit beam returns parallel to the horizontal incident beam. In Figure 7.6 the MRS is undeflected and in Figure 7.7 the MRS is deflected by d [deg.].
The result of arranging the scanners as in Figures 7.6 and 7.7 is a doubling of the horizontal optical scan angle. Other configurations have been applied to this approach to achieve a tripling in the horizontal direction and simultaneously a doubling in the vertical direction [45].
The mirror is actually a rectangular section of a spherical mirror with radius of curvature -100 [mm]. The negative sign denotes concavity. Dimensions of the mirror are given in Table VII.1.
The mirror collimates the individual ray bundles which are focused at the focal point of the mirror. The mirror also angularly magnifies the scan by a factor of 1.6. The ray bundles now reflect off the mirror onto the beamsplitter/combiner. The beam splitter is a 2 [mm] thick parallel plate beamsplitter which is anti-reflection coated on one side to reduce double reflections. 40% of the remaining light, or 24% of the energy present in the original scan, is then reflected into the eye. As the beamsplitter is 60% transmissive, the natural surroundings are also seen by the viewer. The combination of the scanner and the viewing optics generate a scanned raster on the retina which is perceived as a
40 [deg.] horizontal by 30 [deg.] vertical virtual image. It is the aspect of seeing the outside environment and the virtual environment simultaneously which creates an environment of augmented vision.