Starlight arrives at a telescope as a plane wave. A conventional telescope is guided to face the plane wave. Our Primary Objective Grating (POG) takes advantage of the earth’s rotation. The concept is to view the sky as a spectral spread where wavelength is correlated with incident angle i. Under this regime, a secondary telescope does not have to change the angle r at which it receives dispersed radiation in order to acquire a spectrum. A target’s transit along the axis of diffraction will provide a sequence of wave lengths over time to form a spectrum.

A. Parabolic mirror B. POG C. Slit D. Disperser E. Spectra

The night sky arrives at a plane grating and is dispersed sideways toward a parabolic mirror. At grazing angles, a plane grating shows an anamorphic magnification feature. For example, at a grazing angle r = 89°, a 10 meter secondary parabolic mirror can intersect the wave front from a kilometer length grating. The collection area of such a POG would be 10,000 square meters. After the POG, all optics could be conventional including the adaptive optics. Any telescope with a secondary spectrometer pointed at a grazing angle to a POG can serve as a model. A parabolic mirror focuses the light to a slit. A secondary spectrometer separates overlapping spectra from each other. There are many options for spectrometer design. Our simplified schematic above shows a prism.

What differs from convention is the subsequent data reduction. It is common for the image at the slit of a telescope spectrometer to be restricted to a single object, because each object contains a complete spectrum. Any competing object would contaminate that spectrum with metamers. However, with double dispersion, first with the POG and then with a secondary spectrometer, only one wave length is available per object, and multiple objects can be entered into the slit. Holographic double diffraction has been reported. [Lunazzi]

When the POG is a high frequency holographic grating, such as the 600 nm pitch grating at grazing at r = 87° analyzed in this graph, free spectral range can be as much as 400 nm over 40° of elevation. On the other hand, the angular field-of-view in the non-diffraction axis is determined by the secondary parabolic mirror, perhaps no more than 1°. In this anamorphic magnification regime based on plane gratings, one dimension is encoded by diffraction into wavelength while the other dimension is magnified conventionally with a parabolic mirror. POG resolving power balances nicely with the angular resolution of the mirror.

A strip of the sky (above) would appear at the secondary spectrometer sensor array as a coherent image encoded by color (below, background removed for clarity of image).

The spectrum of any one object is assembled over a series of frames as its transit parades it through the entire gamut of wavelengths available to the spectrometer. The illustration below shows three sample frames. A single object is targeted at the cross hairs, and it is circled in the parade of objects in the spectra to the right.

Spectral resolution is tied to sample times set by frame rates. The rate of the parade is determined by the orientation of the POG relative to the rotation of the platform. Integration time will be further discussed in a later section of this proposal under the heading, “What is the flux collection available from a POG as compared to a mirror?”

Angular resolution along the diffraction axis is also set by the frame time, but the theoretical limit of angular resolution on this axis is correlated to grating length. The theoretical limit of resolving power for a grating of kilometer length at visible light wave lengths is in excess of a billion where Dl ~ 10^-5 Å. The correlated angular resolution is on the order of 0.0001 arc seconds. For typical interstellar observations, flux limitations will prevail over the angular resolution, but bright objects can be segregated at 0.05 arc seconds, a window needed to extinguish a host star’s illumination in exoplanets surveys.

Angular resolution in the non-dispersed axis is diffraction limited by the diameter of the secondary parabolic mirror. While the optical physics are well understood for the diffraction limit, the engineering problems are on-going for achieving the diffraction limit on the scale of ELT mirrors. The parabolic mirror secondary to a POG does not need to be moved. It can enjoy a static pose in a sheltered enclosure, suggesting that it can be made larger and maintained more easily than any mirror designed for a motion platform.

Magnitude	Example	Stars / degree^2	1° x 90°	Stars to this magnitude
-1.42	Sirius			1
6.5	Yale catalog			6,500
10.5	Hipparchus cat	3	270	110,000
12	3" scope	12	1,080	500,000
13	6" scope	25	2,250	1,000,000
14	10" scope	60	5,400	2,500,000
15.5		300	27,000	10,000,000
20.5		30,000	2,700,000	1,000,000,000
23	Best scope	300,000	27,000,000	10,000,000,000

The number of objects that can be surveyed over the course of a night is correlated to the size of the strip in degrees² and the flux sensitivity of the instrument. If the instantaneous field-of-view along the diffraction axis is 30°, a night’s observation might span 90°. The other axis, determined by the field-of-view of the parabolic reflector, might be 1°. As a table based on eye sight sensitivity shows, the one night potential far exceeds the capabilities of any MOS devices contemplated for any survey telescope.

Surface relief reflection gratings in grazing exodus configuration polarize most radiation into the TM band. Efficiencies for combined TE and TM first-orders peak at 40% depending on coating conductance according to PCGrate^®. Groove profiles are sinusoidal and shallow at a depth of only 10% of groove length. 90% efficiencies can be obtained in transmission by stacking sequential gratings and by narrowing the bandwidth, particularly in evanescence where the radiation is tunneled into the substrate.

Rotation along the axis of diffraction, that is to say tipping the short axis, will access the entire sky. Observations can be made with a POG locked down. The POG’s ribbon-like aspect ratio is readily segmented and lends itself to auto collimation. Alignment of segments is a known art from microlithography where grating fiduciaries are routinely used to achieve nanometer trace alignments at assembly line speeds.

This is a new class of telescope with a plethora of embodiments outside the literature. It can be implemented with any conventional telescope pointing below the horizon at a ground-level reflective POG or from below ground pointing at a ground-level transmission POG. The latter embodiment would be completely sheltered.

We have a ZEMAX model of a 300 x 10 m reflective POG where the secondary is a 15 m parabolic mirror with a 150 m focal length, and the spectrometer is a 150 m holographic grating[1] with a resolving power matched to the large POG. Grazing exodus is 87.9°. The model shows a 30° field-of-view in the diffraction axis over the free spectral range of 400 to 700 nm. Incident wave lengths are color coded in red, green and blue.