Matthew McGill and Richard Rallison
A novel holographic optical element designed by NASA allows use of a linear array detector to record the fringe pattern of a Fabry-Perot.
Diffractive optical elements (DOEs) are designed and used to redirect light based on the properties of diffraction via periodic structures or periodic changes in the properties of an optical material. Diffraction itself is a highly-dispersive phenomenon whereby the direction of scattered light is determined primarily by the spatial frequency of the periodic structure, combined with incident angle and wavelength. The dispersion is so great that DOEs are almost always used with monochromatic or laser light. No matter how complex the pattern they diffract, DOEs can be thought of as a spatial array of small diffraction gratings or a superposition of many plane gratings over an aperture. Often, a DOE is patterned such that many local areas perform different optical tasks, somewhat like an integrated circuit. In fact, many DOEs are fabricated by the same machines used to make microelectronics. It is possible to reshape light and redistribute the energy in the light in an almost endless variety of ways, and DOEs can be used to create optical transformations that are not possible using conventional optics.
Holographic optical elements (HOEs) are a subset of the DOE family. In essence, HOEs are holographic DOEs, generated by the overlapping of plane, spherical, conical, and pre-aberrated waves (holography, for example) to create an interference pattern that is recorded in any of a dozen or more media that will transform intensity distributions into phase distributions. The phase variations can occur along the surface or through the volume. Compared to DOEs, the spatial frequencies of HOEs are typically much higher, and the attainable physical sizes are larger. We have developed a spatially-multiplexed HOE to solve a specific problem in remote sensing. It has been fabricated in a volume phase material and subsequently capped with an AR-coated cover glass, making it rugged and cleanable with low insertion losses.
The measurement need
Global measurement of the atmospheric wind field is an important but unfulfilled measurement need within the atmospheric science community. Light intensity detection and ranging (lidar) is a type of active remote sensing used to measure properties of the atmosphere such as wind, water vapor, and cloud optical properties. Light transmitted from a laser is backscattered by aerosols and molecules in the atmosphere (see Fig. 1). The backscattered signal is collected by a telescope and passed to a receiver system. Specifics of the receiver design depend on the atmospheric variable to be measured.
When light is scattered by moving particles, a Doppler shift is imparted relative to the incident wavelength. In the atmosphere, we can assume that aerosols and molecules are advected along at the mean wind speed. Thus, the Doppler shift imparted to the backscattered photons provides a measure of wind speed. A wind speed profile requires that detectors and electronics take readings and reset within microseconds. By timing the return signal, the backscattered signal is correlated with the distance from the lidar transmitter to the scattering particles.
To measure atmospheric wind profiles, the lidar receiver must be capable of resolving the small Doppler shifts characteristic of atmospheric motions. For example, at visible wavelengths, typical wind speeds induce Doppler shifts of about 10-5 nm. A Fabry-Perot interferometer (FPI) is typically used to adequately resolve these small spectral shifts.
Doppler shifts in the optical spectrum can be detected either by coherent (heterodyne) or direct-detection lidar systems. Coherent systems mix the return signal with a local oscillator and observe changes in the resultant beat frequency. Direct-detection systems are spectroscopic instruments that directly observe the spectral shift using, for example, an FPI. A particular type of direct-detection Doppler lidar called fringe-imaging resolves the spectral shape of the backscattered Doppler-shifted signal.1 The Doppler-shifted spectrum is then compared to the unshifted spectrum of the outgoing laser light (see Fig. 2). The measured wavelength shift is directly proportional to the line-of-sight wind speed.
A problem then presents itself: how to efficiently measure the spectral output of the FPI. For non-lidar applications, charge-coupled detectors (CCDs) monitor the FPI output, but CCDs cannot operate at the microsecond time increments necessary for range-resolved lidar measurements. Thus, it becomes necessary to somehow compress the FPI output to a manageable format without loss of signal and without introducing any frequency blurring.
The HOE used with Fabry-Perot interferometers
The fringe-imaging Doppler lidar technique is well known and proven, but detection options have been expensive, complex, and inefficient.2 Our goal was to develop a method of efficiently measuring the radial output of the FPI that provided a simple, inexpensive detection alternative for FPI-based systems. We developed an HOE that transforms a circular Fabry-Perot fringe pattern into a series of point images. Individual solid-state detectors or a linear-array detector can be placed at the image plane, thereby providing an efficient, spectrally resolved measurement of the FPI output.
Visually the HOE looks like a zone plate, but unlike a zone plate, each annulus of the HOE acts as a separate, off-center lens. The hologram itself serves as a field lens, and the light incident on each annulus is spatially separated from the other annuli. The HOE redirects all the rays that enter each of the circular annuli into unique off-axis focal points (see Fig. 3). Each annulus is simply an off-axis focusing DOE that gets shifted laterally by some arbitrary increment between zones. The focus is located off the axis of rotation and out of the path of any zero-order light.
To match the Fabry-Perot fringe pattern, the annuli are designed to intercept equal wavelength intervals. If created carefully, there is no crosstalk between image points. The rays for a given annulus do not converge to a real image point. In fact, the rays actually diverge from the plate. There is, however, a localized point in space where all the diverging rays from a given annulus intersect (see Fig. 4). By nature, the HOE gives the smallest image points when used with collimated or near-collimated light. Incident light with a larger range of angles causes the image points to grow and distort, but collecting optics can be used to capture the light from each spot and focus it onto a detector. The choice of wavelength, image spacing, and image pattern are particular to the design.
Construction of the HOE is similar to construction of any holographic lens except for the masking required to create the annuli. A master hologram is recorded and then each annulus is individually exposed through the master hologram. The substrate with the holographic emulsion is moved between exposures to give spatial separation between the image points in a process called spatial multiplexing. By design, the image points all share a common focal plane and lie in a straight line. The HOE shown in Figure 4 is recorded in a 7-µm-thick DCG emulsion spun onto a thin glass substrate. Processing is done in water and alcohol followed by a bake-out and then capping between two AR-coated cover slides.
Initial results meet expectations
The primary concern for our application is the diffraction efficiency of the HOE. For Doppler lidar, every photon counts. An inefficient HOE would provide no improvement over other detection options. A secondary concern is image size, although this requirement can vary greatly depending on the detectors to be used. Our current goal is to use a Hamamatsu linear-array detector with custom integrating electronics to operate in photon-counting mode.
Recent versions of our HOE have diffraction efficiency in excess of 80%. This means more than 80% of the light incident on the HOE gets to the detector. Light that doesn't converge to the image points appears in several locations: some is transmitted directly through the plate (zero-order), some is sent into a negative order, and some is reflected. When tested in collimated light using an extended source, the image points all met our requirement of 150-µm diameter. The individual annuli do not overlap and neither do the focused spots, so there is no crosstalk between the image points.
Collimated light produces the smallest image spots, but the HOE is intended for use in a system with slightly divergent light. Further, in a Doppler lidar system, the receiving telescope is fiber-coupled to the receiver optics. Therefore, the light originates from an extended object and thus simultaneously from many points. The focus is degraded by the need to re-image the fiber-end onto the detector. The fiber is large and the focus can never be smaller than the demagnified image of the fiber. To further reduce spot sizes would require making the fiber smaller or rearranging the imaging optics to demagnify the fiber end.
The HOE shown in Figure 4 has been successfully coupled with an FPI. Work is now underway to demonstrate validated wind measurements using the HOE and FPI combination. Successful demonstration will subsequently lead to ground-based or airborne demonstrations.
ACKNOWLEDGEMENT
This work is supported by the Technology Commercialization Office at Goddard Space Flight Center. For more information, contact Joseph Famiglietti, Technology Commercialization Office, Goddard Space Flight Center, Mailstop 750, Greenbelt, MD 20771.
REFERENCES
- M. J. McGill et al., Appl. Opt. 36, 1928 (1997).
- T. L. Killeen et al., Appl. Opt. 22, 3503 (1983).
MATTHEW MCGILL is a research scientist at NASA's Goddard Space Flight Center, Code 912, Greenbelt, MD, 20771; email: [email protected]. RICHARD RALLISON is president of Ralcon Development Laboratory, 8501 S. 400 W., Box 142, Paradise, UT 84328; email: [email protected].