Optoelectronic System Design Final Project

Transcription

1 Optoelectronic System Design Final Project Max Colice Optoelectronic Computing Systems Center Department of Electrical & Computer Engineering University of Colorado Boulder, CO (303) December 12,

2 1 Problem Description As described in earlier documents, this system will transmit a signal from a ground-based station to a satellite in geosynchronous orbit. The satellite will retroreflect the beam, now modulated at a lower frequency. The high level block diagram in Figure 1 describes system operation. Data In Background Noise Data In Modulated Laser Trans./Rec. Multiplexing Scheme Ground-based Telescope Air & Space Space-based Telescope Retroreflector w/detector & Modulator Electronics Detector Data Out Data Out Figure 1: High level system block diagram. The dashed box indicates the portion of interest. This document contains a detailed design analysis of the ground-based and space-based telescopes and of the retroreflector, as indicated by Figure 1. It will also provide external specifications for all detectors, modulators and the laser itself. 2 Draft Specifications This system must transmit a beam modulated at MHz rates from the Earth s surface to a satellite orbiting the Earth at an altitude of approximately 42,000 km (geosynchronous orbit). The received signal must be sufficiently strong so as to achieve a Signal-to-Noise Ratio (SNR) of 10 db. The system will use an optical carrier at wavelength of 1.55 µm to take advantage of the atmospheric absorption window in the infrared. The satellite-based receiver will retroreflect the beam to its point of origin. The retroreflected beam will be modulated at khz rates. The system should be portable and mounted such that the user can achieve pointing stability to better than 10 murad. The gound-based portion of the system should be operable over a reasonable temperature range (0 C to 50 C). In addition, the retroreflected beam intensity levels should be sufficiently high to achieve a 10 db SNR and low enough to be eye safe. 3 Design Selection As the design selection was discussed in great detail in a previous document (Project Specifications II), it will receive only modest attention below. Direct detection was chosen over coherent detection for reasons of simplicity. Coherent detection has an inherent gain advantage, but it is extremely difficult to phase-lock two sources separated by 42,000 km. Direct detection does not give any gain, but it also does not require exceptional frequency stability or a complicated phase-locking scheme. The retroreflection scheme was also chosen in order to simplify the device design. It eliminates the need for a laser on the satellite, although at a cost in power - no more than the received power 1

3 may be used for retroreflection. This is essentially a stare-stare design; the user points the upward beam in the appropriate direction (possibly determined using GPS triangulation), and the satellite reflects light back down to the user. No complicated scanning mechanisms are required. This sort of system will be lighter, easier to package and longer lived as it has no moving parts. 4 Design As the ground-based and space-based telescopes are widely separated, they will be treated as decoupled systems for the purposes of analysis. The design process will begin with a determination of the laser power level necessary for acheivement of the 10 db SNR goal. The telescopes and multiplexing scheme necessary for the Earth-based transmitter/receiver will then be addressed in detail. 4.1 SNR Determination The received optical power for both telescopes can be determined by means of simple Gaussian optics. Each telescope will be assumed to emit a collimated beam. As the range between telescopes is extremely large, it is not unreasonable to treat the beams impinging on the telescopes as plane waves (i.e., parallel rays). Picking the Earth-based and space-based telescope apertures fixes the collimated beam waists and allows us to calculate the received beam waists as follows. We can start by determining the Rayleigh range, z 0, z 0 = πw2 0 λ where w 0 is the radius of the beam waist and λ is the wavelength. location z can be written as (1) The beam radius at some ( ) z 2 w = w (2) z0 If z z 0, the beam radius may be approximated as w = λz/πw 0. We can next determine the irradiance, E, at z by dividing the optical power contained within this beam radius, P optical, by the area determined by the beam radius. As we know the wavelength of the incident light, we can convert this power into photon flux, φ, through the telescope aperture: φ = λ P optical hc πw 2 πr2 (3) where h is Planck s constant, c is the speed of light in vacuum and r is the radius of either the space-based or the Earth-based telescope aperture (depending on the beam direction). The photon flux generates a mean photocurrent, ī, at the detector, which can be written as ī = qηφ. (4) η is the detector quantum efficiency and q is the electric charge. The SNR is simply the ratio of the power due to this mean photocurrent to the power due to noise sources, SNR = ī 2 σshot 2 + σ2 thermal +. (5) ī2 background 2

4 This analysis considers the effects of shot noise, σ 2 shot, thermal noise, σ2 thermal and noise due to sunlight reflected off the Earth and other stellar bodies. The variances may be written as σ 2 thermal = 4k B T B (6) σ 2 shot = 2qīB, (7) where B is the receiver bandwidth and T is the receiver temperature. The optical power due to reflected sunlight can be written as P background = H background Ω fov A receiver B filter, (8) where H background is the radiance, Ω fov is the solid acceptance angle of the receiver, A receiver is the receiver area and B filter is the spectral bandwidth of the receiver. The solid angle field of view may be approximated as (π/4) (θ rec ) 2 ; θ rec is the angular acceptance of the receiver. 1 This optical power must be converted to an electrical current, as shown above in Equations 3 and 4. SNRs and electrical power levels for both the space-based and Earth-based receivers are plotted over a range of laser optical powers in Figures 2 and 3. All values used in the calculation are listed in the Appendix A. The IDL program used to generate these plots is also included at the end of this report. Figure 2: SNR and electrical power levels for the space-based receiver The space-based receiver SNR reaches 10 db at a laser power of less than 1 mw, while the Earth-based receiver SNR hits 10 db at a laser power of roughly 100 mw. These power levels are well within the reach of modern technology. Note that the space-based receiver is shot noise-limited at 10 4 mw and the the Earth-based receiver reaches the shot noise limit at a laser power of < 10 8 mw. The signal power levels are still fairly low. However, MHz bandwidth Lock-In amplifiers possess dynamic reserves of ge100 db, and may be suitable for use with the Earth-based receiver. Preamplification will definitely be necessary. We will specifiy a minimum laser power level of 1 W (easily obtainable with today s technology). Further analysis is beyond the scope of this document. 3

5 Figure 3: SNR and electrical power levels for the Earth-based receiver 4.2 Earth-based Telescope The Earth-based telescope must expand the laser s output to a diameter of 10 cm to meet our specifications, requiring 100X magnification for a laser output diameter of 1 mm. In addition, it must contain some sort of multiplexing mechanism so that it can separate the retroreflected, Earth-going beam from the transmitted, space-going beam Polarization Multiplexing Polarization multiplexing is relatively simple, requires no moving components and can be easily implemented as the beam will necessarily be reflected at the other end of the link. Laser outputs are usually linearly polarized, although note that an additional polarization element may be needed to further improve the purity of the laser output polarization state. The beam can therefore be converted to circular polarization by means of a λ/4 plate, as illustrated in Figure 4. The beam is then expanded using a telescope. The waveplate is placed in the path of the smaller beam, as the waveplate s cost will increase as its size increases. The retroreflected beam will have the orthogonal circular polarization (the polarization will be flipped upon reflection), and will be converted to the orthogonal linear polarization by the λ/4 plate. The two beams can then be separated by a polarizing beamsplitter; these devices have extinction ratios ranging from 30 db for thin film devices to 45 db for crystal optic devices Thin Lens Design In the thin lens approximation, the telescope consists of two lenses separated by the sum of their focal lengths. The telescope s magnification is given by the ratio of their focal lengths, M Earth = f 2 /f 1. We have taken the laser s output to be perfectly collimated; this is reasonable at this level of approximation. Note that Figure 4 includes an aperture stop at the focal plane of the lenses. As both the space-going and Earth-going beams should be collimated and directed normally to the lens surfaces, a spatial filter may be used to reject light entering the telescope from an angle. The aperture spot should be no larger than the larger of the minimum spot sizes of the two lenses. If the lenses have matched numerical apertures (NAs), then their spot sizes will be identical. Minimizing the spot size will improve the system s ability to reject stray light. However, 4

6 f 1 f 2 Data In Polarizing Beamsplitter Spectral Filter λ /4 Space-going Beam Modulated Laser Polarization States Detector Earth-going Beam Data Out f 1 Aperture Stop f 2 Polarization States Figure 4: Schematic representation of the Earth-based telescope the lenses with larger NAs tend to have worse aberration performance, increasing the resolvable spot size past the diffraction limit. We will compromise by selecting moderately fast lenses for use in the Earth-based telescope. Spectral filtering also reduces noise levels ZEMAX Design It is very difficult to achieve diffraction-limited 100X magnification with only 2 lenses, as the primary lens must be somewhat aggressive and the secondary must be long focal length. As we would like to achieve good beam quality with short total length ( 0.5 m), it becomes easier to use a set of 10X Galilean telescopes in series. Galilean telescopes possess no internal focus, thereby precluding the spatial filtering scheme described above. However, another pair of Fourier transform lenses inserted between the 10X telescopes may be used to implement this scheme. A baffle may also be used to limit the telescope field of view. ZEMAX was used to create the Earth-based telescope design. The second 10X telescope was created first by using an entrance pupil diameter of 1 cm and a pair of custom singlets. A paraxial lens was used to focus the telescope s output to the image plane. Optimization was performed using the default merit function in conjunction with an additional constraint: the height of the beam impinging on the paraxial lens was forced to 5 cm (the output beam radius). The lens separation was fixed at 500 mm. Once this optimization was completed, the first 10X telescope was introduced and the entrance pupil diameter was stopped down to 1 mm. A similar optimization routine was run to set the first telescope s lens parameters, etc. Further results, including a layout, are included in Appendix B. The ZEMAX Lens Data Editor window is shown below in Figure 5. The system achieves good performance in a total lenght of 575 mm. 4.3 Space-based Telescope As stated above, the space-based and Earth-based telescopes are separated by such a large distance that they can be treated as decoupled systems. The space-based telescope will see parallel rays impinging on its first surface. 5

7 Figure 5: Earth-based telescope ZEMAX Lens Data Editor window Functional Design The space-based telescope is functionally the same as the Earth-based telescope; as shown in Figure 6, it consists of a beam collapser that sends its output to a retroreflecting prism. The magnification is given by M space = f 4 /f 3. A pinhole located at the interelement focal plane serves to limit the receiver s angular bandwidth, thereby eliminating additional background light and improving the SNR. f 3 f 4 Space-going Beam Retroreflector w/ Detector & Modulator Polarization States Data In Data Out Earth-going Beam Aperture Stop f 4 f 3 Figure 6: Schematic representation of the space-based telescope The desired angular bandwidth will determine the minimum spot size and pinhole size. The space-going beam s the angular deviation will be less than 10 µrad for a waist of w 0 = 5 cm. We can determine the minimum aperture radius, r space, necessary for achieving this angular resolution by applying the Rayleigh resolution limit. Recall that the diffraction limited spot size radius is given by ρ = 0.61λ f. (9) r space Applying simple trigonometry allows us to find r space = 9.46 cm. We have chosen r space = 5 m, as indicated in Table 1 to improve light collection efficiency, and easily satisfy this limit. 6

8 The retroreflecting scheme relies on some sort of combination detector/modulator, which could take one of several forms. It could be a detector array located intelligently on a quarter-wave push-pull modulator. Alternatively, it could take the form of a quantum well device, such as that proposed by Gilbreath et al. 2 We will specify that its receive bandwidth be 1 MHz and that its transmit bandwidth be 1 khz. Note that the SNR calculation performed above did not take into account loss due to photodetection. However, it is reasonable to suggest the 50% of the light is absorbed and the other 50% is reflected. This would uniformly depress SNR values by 3 db Thin Membrane Mirrors It is not practical to build 10 m diameter lens for use in space. Solid mirrors of the same diameter also exceed size and weight limits imposed by modern rockets - the Hubble Space Telescope has a main mirror diameter of only 2.4 m. 3 However, it has been proposed that thin film membranes could be used to construct large mirrors in space. 4 Such membrane mirrors would consist of a thin, reflective membrane, such as mylar or a variant thereof, stretched across a support structure. They would have low densities and could be folded, making it practical to launch mirrors with much larger diameters than those built using conventional techniques. The membrane thickness must be controlled to within 0.1 µm in order to meet minimum requirements for imaging optics; this is not an unreasonable goal, as membranes with a thickness ripple of ±1µm over lengths of 2 m were available commercially as of Adaptive curvature could be induced by means of electrostatic pressure. 4 This technology could easily allow us to increase the aperture size to our current target of 10 m Cat s Eye Retroreflectors Cat s-eye retroreflectors offer several advantages over lens/mirror and corner cube retroreflectors. We have already determined that we don t wish to launch large lens into space. Hollow corner cube reflectors typically consist of a minimum of three plane mirrors arranged in a threefold rotationally symmetric fashion. We would probably need to demagnify the incident beam in order to use a hollow corner cube. Large solid corner cubes (i.e. prisms) are too heavy to lift into orbit. Cat s-eye retroreflectors can be fabricated from two curved mirrors, with the secondary sitting at the focus of the primary. This greatly simplifies the optical design. 6 In addition, the modulator/detector can be placed at the beam focus, thereby reducing the size of the device. 7 Bear and Marjaniemi propose using a parabolic primary mirror in conjunction with a spherical secondary mirror with a power roughly twice that of the primary. 6 As before, ZEMAX provides a convenient way to optimize the system design. In this case, an f/5 parabolic mirror of 10 m diameter was placed in the path of an axial beam of the same diameter. ZEMAX s default merit function was used to optimize the mirror s curvature and placement with respect to the image plane. Next, a small spherical mirror was placed at the image plane, and the rays were redirected off of the primary mirror onto a paraxial lens. Note that the secondary mirror also serves as a spatial filter; beams outside the angular bandwidth of the system will be focused to points off the mirror s surface. Circular obscurations were placed in the path of the incoming and outgoing beams to compensate for the present of the spherical secondary. The spherical mirror curvature was then optimized to provide diffraction-limited performance using the default merit function. The ZEMAX Lens Data Editor window is shown in Figure 7. Please refer to Appendix C for system layout information and perfomance plots. Note that the two mirrors are separated by a distance greater than 200 m. A single satellite of such size would have to be constructed in orbit. However, the two mirrors could be located separate spacecraft in concentric orbits. 7

9 Figure 7: Space-based telescope ZEMAX Lens Data Editor window 5 Tolerance and Packaging 5.1 Earth-based Telescope The two 10X telescopes that comprise the Earth-based telescope will be sensitive to interlens spacing errors. Of the two, the first telescope is ten times smaller, and therefore ten times as intolerant to absolute variations in spacing, tilt, etc. Lens tilt will send the beam off at some aribitrary angle, making the external pointing mechanism (i.e. GPS pointing) inaccurate. The intertelescope spacing should be insensitive to longitudinal movement, but a transverse shift will also result in inaccurate pointing. 5.2 Space-based Telescope As discussed in Beer and Marjaniemi, 6 the cat s-eye retroreflector is relatively insensitive to misalignment. A full-sized secondary mirror would give retroreflects rays up to an incident angle of 10 (recall that our divergence angle is < 10µrad). Therefore tilt of the secondary with respect to the secondary is not terribly important. However, transverse misalignment will shift the central angular frequency. Longitudinal misalignment will be difficult, and will result in decreased angular resolution through misfocus. Pointing is also an issue; however, it is assumed that another class of engineers knows how to get satellites to point towards Earth with acceptable accuracy. References [1] S. G. Lambert and W. L. Casey, Laser Communications in Space. Artech House, Boston, 1995 [2] G. C. Gilbreath et al., Large-aperture multiple quantum well modulating retroreflector for free-space optical data transfer on unmanned aerial vehicles, Opt. Eng. 40 (7), (2001) [3] [4] R. Angel, J. Burge, K. Hege, M. Kenworthy and N. Woolf, Stretched membrane with electrostatic curvature (SMEC): A new technology for ultra-lightweight space telescopes, UV, Optical, and IR Space Telescopes and Instruments, J. B. Breckinridge and P. Jakobsen, eds., Proc. SPIE 4013, , Munich,

10 [5] B. Stamper, R. Angel, J. Burge, and N. Woolf, Flat Membrane Mirrors for Space Telescopes, Imaging Technology and Telescopes, J. Breckinridge, ed., Proc. SPIE 4013, 2000 [6] R. Beer and D. Marjaniemi, Wavefronts and Construction Tolerances for a Cat s-eye Retroreflector, Appl. Opt. 5 (7), (1966). [7] M. L. Biermann, W. S. Rabinovich, R. Mahon and G. C. Gilbreath, Design and analysis of a diffraction-limited cat s-eye retroreflector, Opt. Eng. 41 (7), (2002). 9

11 A SNR Calculation Parameters Table 1: Space-going Beam Parameters Parameter Value Geosynchronous Orbital Distance, z 42,000 km Operating Wavelength, λ 1.55 µm Laser Output Radius, r laser 0.5 mm Transmit Aperture Radius, w 0 5 cm Rayleigh range, z m Beam Radius in Space, w m Receive Aperture Radius, r space 0.5 m Angular Deviation 9.86 µrad Detector Temperature, T space 10 K Detector Bandwidth, B space 1 MHz Spectral Filter Bandwidth, B filter 1.0 nm Stellar Radiance, H background 210 W/m 2 /Sr/µm Table 2: Earth-going Beam Parameters Parameter Transmit Aperture Radius, w 0 Rayleigh Range, z 0 Beam Radius on Earth, w Receive Aperture Radius, r Earth Angular Deviation Detector Temperature, T Earth Detector Bandwidth, B Earth Value 5 m m m 0.05 m µrad 300 K 1 khz 10

12 B Earth Telescope Design Figure 8: 3D Layout Figure 9: Optical Path Difference Figure 10: Ray Fan Figure 11: Diffraction Encircled Energy Figure 12: Spot Diagram 11

13 C Space Telescope Design Figure 13: 3D Layout Figure 14: Optical Path Difference Figure 15: Ray Fan Figure 16: Diffraction Encircled Energy Figure 17: Spot Diagram 12