Electronic polar alignment for astronomical instrument

A technique for polar aligning the mount of a telescope or other astronomical instrument includes acquiring star images from an electronic polar scope and determining a location of a celestial pole relative to the star images based on computerized matching of the star images to information in a database. The mount has a right-ascension (RA) axis, and the technique directs an adjustment to the mount so as to align a location of the RA axis with the determined location of the celestial pole.

BACKGROUND

Many equatorially mounted telescopes and other instruments require polar alignment to perform as designed. As is known, polar alignment is a process whereby an equatorial mount is positioned and adjusted so that the mount's right ascension (RA) axis runs parallel to the Earth's axis of rotation. Once polar aligned, an equatorial mount can compensate for the Earth's rotation merely by counter-rotating the mount about the RA axis at a rate of approximately once per day. Many equatorial mounts include clock drives to provide the needed rotation. A clock-driven, polar-aligned, equatorially-mounted telescope can keep a celestial object approximately centered in the telescope's field of view over a long observing session.

The ability to keep an object centered depends largely on the accuracy of polar alignment. The more accurate the alignment, the fewer corrections have to be made over time. Accurate polar alignment is essential for effective go-to operation, as a telescope that is not properly aligned cannot locate objects automatically based on celestial coordinates. It is also essential for good astrophotography, where exposure times can reach multiple hours.

To promote accurate polar alignment, many equatorial mounts include built-in polar scopes, i.e., small telescopes mounted coaxially with the mounts' RA axes. Some polar scopes include illuminated reticles that display star images or other patterns, which the user can see superimposed on actual stars. The user can adjust the mount (e.g., in altitude and azimuth) and rotate the reticle so that the stars as viewed through the polar scope line up with the pattern on the reticle. An example of this type of polar scope and alignment is disclosed in U.S. Patent Publication No. 2012/0307356A1, the contents and teachings of which are incorporated herein by reference in their entirety.

SUMMARY

Unfortunately, prior approaches to polar alignment can pose challenges to users. Not least of these is the need for a user to adjust a mount's altitude and azimuth while simultaneously looking through a polar scope and turning a reticule in the dark. As polar scopes are almost always pointed up (toward the North Celestial Pole in the Northern Hemisphere or toward the South Celestial Pole in the Southern Hemisphere), it can place a strain on the user's neck to have to look up, especially when the polar scope is low to the ground, as it often is. In addition, it can be difficult for many users to achieve good alignment accuracy. Lining up stars with reticule images can take some practice, and errors can arise if the user's eye is not perfectly aligned with the polar scope. Thus, it would be desirable to provide a polar scope and methodology that is easier for users and more consistently accurate.

In contrast with prior approaches, an improved technique for polar aligning the mount of a telescope or other astronomical instrument includes acquiring star images from an electronic polar scope and determining a location of a celestial pole relative to the star images based on computerized matching of the star images to information in a database. The mount has a right-ascension (RA) axis, and the technique directs an adjustment to the mount so as to align a location of the RA axis with the determined location of the celestial pole.

Certain embodiments are directed to a method of polar aligning a mount for an astronomical instrument. The method includes acquiring star images from an electronic scope coupled to or integral with the mount and determining a location of a celestial pole relative to the star images, based on computerized matching of the star images to information in a database. The method further includes displaying, by a computing device operatively connected to the electronic scope, the star images superimposed with a first symbol and a second symbol, the first symbol indicating the determined location of the celestial pole relative to the star images, the second symbol indicating a location at which a right ascension (RA) axis of the mount intersects a field of view of the electronic scope, the mount becoming polar aligned responsive to the first symbol intersecting the second symbol.

Other embodiments are directed to a mount for an astronomical instrument. The mount includes a right-ascension (RA) axis, an electronic scope oriented substantially parallel to the RA axis, and a set of non-transitory, computer-readable media having instructions which, when executed by a computing device, cause the computing device to perform a method of polar aligning the mount, such as the method described above. Still other embodiments are directed to a computer program product. The computer program product stores instructions which, when executed by a computing device, cause the computing device to perform a method of polar aligning the mount, such as the method described above.

The foregoing summary is presented for illustrative purposes to assist the reader in readily grasping example features presented herein; however, this summary is not intended to set forth required elements or to limit embodiments hereof in any way. One should appreciate that the above-described features can be combined in any manner that makes technological sense, and that all such combinations are intended to be disclosed herein, regardless of whether such combinations are identified explicitly or not.

DETAILED DESCRIPTION

Embodiments of the improved technique will now be described. One should appreciate that such embodiments are provided by way of example to illustrate certain features and principles but are not intended to be limiting.

An improved technique for polar aligning the mount of a telescope or other astronomical instrument includes acquiring star images from an electronic polar scope and determining a location of a celestial pole relative to the star images based on computerized matching of the star images to information in a database. The mount has a right-ascension (RA) axis, and the technique directs an adjustment to the mount so as to align a location of the RA axis with the determined location of the celestial pole.

FIG.1shows an example environment100in which embodiments of the improved technique can be practiced. The environment100includes a mount102having an RA axis110and a declination axis120. The mount102sits on a stand130, such as a tripod or pedestal. The mount102also has an adapter140, such as a dovetail clamp, configured to receive an optical assembly (not shown). The optical assembly may be a telescope, a camera, or some other astronomical instrument. A declination shaft122extends along the declination axis120, and a counterweight124attaches to the declination shaft122. The counterweight124is configured to be slid to different locations along the declination shaft122, so as to balance the weight of the optical assembly (and any additional equipment) across the RA axis110. The mount102includes an adjustable wedge150having adjustments152, such as knobs. The adjustments152enable the angle of the mount102to be varied in both altitude (up and down) and azimuth (left and right).

As further shown inFIG.1, an example electronic polar scope160is attached to or integral with the mount102and is oriented substantially parallel to the RA axis110. In the example shown, the electronic polar scope160is permanently installed coaxially with the RA axis110. The electronic polar scope160is configured to receive light from the forward direction of the RA axis110, to focus the light, and to generate images of objects. In the arrangement shown, the mount102includes an aperture162for allowing light to pass unobstructed to the electronic polar scope160. The aperture162may be a hole or a transparent cover, for example.

A computing device170operatively connects to the electronic polar scope160, e.g., via a cable180, for controlling the electronic polar scope160and for reading back image data and settings. In some examples, the computing device170separately connects to the mount102via another cable182, e.g., for controlling positioning and tracking of the mount102and/or for performing other functions. In an example, the mount102is a go-to mount, meaning that it includes motors for automatically driving the RA and declination axes to specified coordinates. This is not required, however, as the mount102may be any equatorial mount or other mount that can be adapted for equatorial tracking.

The computing device170may be any computerized apparatus capable of running software, displaying images, and communicating with the electronic polar scope160, such as a laptop computer, desktop computer, tablet computer, smart phone, PDA (Personal Data Assistant), or the like. Cables180and182may be USB (Universal Serial Bus) cables, RS-232 cables, RS-422 cables, Ethernet cables, telephone cables, or the like. There is no need for the cables180and182to be of the same type. In some examples, the electronic polar scope160may employ wireless communication, such as Wi-Fi and/or Bluetooth, and the computing device170may connect to the electronic polar scope160wirelessly, i.e., without the need for cables180and182.

In example operation, a user places the mount102on its stand130at a desired site. The user orients the mount102in such a way that its RA axis110points roughly in the direction of a celestial pole, e.g., to within about 5 degrees of Polaris in the Northern Hemisphere or of Sigma Octantis in the Southern Hemisphere. The user might level the mount102, which is not required for polar alignment but might be needed for go-to operation. The user plugs in the cable180(and optionally the cable182) and starts a software application on the computing device.

Once running, the software application initializes communication with the electronic polar scope160. In some examples, the software application at this time directs the user to block a lens of the electronic polar scope160, e.g., by applying a cap or other cover to the aperture162. The user covers the aperture162and directs the software application to continue. The electronic polar scope160then acquires a set of dark frames, i.e., one or more frames that provide output from the polar scope160in the absence of incoming light. In an example, the application averages the output for each pixel location over multiple dark frames and thereby produces a respective average reference level for each pixel location. Reference levels typically vary over temperature and from one pixel to the next. The reference levels can later serve as corrections for raw image data, e.g., by subtracting reference levels from respective raw pixel values. In an example, the application also uses dark frames for identifying dead pixels and/or stuck pixels. With the dark frames acquired, the application directs the user to uncover the electronic polar scope160. The user complies and the electronic polar scope160proceeds to acquire star images.

The application displays the star images, preferably corrected for reference levels, on a screen or monitor172of the computing device170. The application also attempts to match the star images to information in a database. The database stores coordinates of stars in a vicinity of the celestial pole (or of both celestial poles), e.g., within about 20 degrees of the pole (or of each pole). In an example, the application performs plate solving and/or other image analysis to identify stars that are detected in the star images. In general, plate solving can be completed by identifying as few as four stars. Based on the image analysis, the application determines a location of the celestial pole relative to the star images. For example, and without being limiting, the application matches stars detected in the star images to stars whose coordinates are stored in the database, computes an angular offset between the matched stars in the database and the celestial pole, transforms that offset into a coordinate system of the electronic polar scope160, and locates the celestial pole in the displayed images based on the transformed offset. The application then displays a symbol over the star images that indicates the determined location of the celestial pole.

In some examples, the application stores an RA pixel coordinate at which the RA axis110intersects the field of view of the electronic polar scope160. Here, the “field of view” is the displayed area that corresponds to a two-dimensional pixel array located at the focal plane of the electronic polar scope160. Small errors inherent in the electronic polar scope160and/or in the mount102may cause the RA pixel coordinate to vary from a perfect center of the field of view. One should appreciate, however, that the RA pixel coordinate is a stable characteristic of the system and does not change as long as the mechanical configuration remains constant. In an example, the RA pixel coordinate is factory-determined and encoded within the software application itself. Alternatively, the RA pixel coordinate may be stored in the electronic polar scope160and/or may be provided in a separate paper, email, or the like. For example, the user may obtain the RA pixel coordinate in an email from a manufacturer or distributer and manually transfer the coordinate to the application, which then persistently stores the coordinate as part of the application.

When displaying the symbol that indicates the celestial pole, the application may also display a symbol that indicates the RA pixel coordinate. This may be accomplished easily as the RA pixel coordinate is merely a fixed location in the pixel array. The application then directs the user to adjust the mount (e.g., via adjustments152for altitude and azimuth) to bring the two symbols into alignment with each other. When the user has successfully aligned the two symbols, the mount102has become accurately polar aligned.

In the manner described, accurate polar alignment can be achieved easily, without stressing the user's skills or straining the user's neck. The user can complete the alignment while standing or sitting in a comfortable position. There is no need to rotate any reticle or to visually line up any features other than the two symbols, which can be rendered onscreen for easy visualization.

FIG.2shows the example computing device170in additional detail. As shown, the computing device170includes the display172, one or more communication interfaces210, a set of processors220, and memory230. The display172may be a computer monitor, screen, television, touch screen or the like. The communication interface(s)210include, for example, one or more USB interfaces, RS-232 interfaces, RS-422 interfaces, Ethernet interfaces, Wi-Fi interfaces, Bluetooth interfaces, and/or the like. The processor(s)220may include one or more processing chips and/or assemblies. The memory230includes both volatile memory, e.g., RAM (Random Access Memory), and non-volatile memory, such as one or more ROMs (Read-Only Memories), disk drives, solid state drives, and the like. The processor(s)220and the memory230together form control circuitry, which is constructed and arranged to carry out various methods and functions as described herein. Also, the memory230includes a variety of software constructs realized in the form of executable instructions. When the executable instructions are run by the processor(s)220, the processor(s)220carry out the operations of the software constructs. Although certain software constructs are specifically shown and described, it is understood that the memory230typically includes many other software components, which are not shown, such as an operating system, various applications, processes, and daemons.

The software constructs in the memory230, or portions thereof, may be embodied as a computer program product including one or more non-transient, computer-readable storage media, such as a magnetic disk, magnetic tape, compact disk, DVD, optical disk, flash drive, solid state drive, SD (Secure Digital) chip or device, Application Specific Integrated Circuit (ASIC), Field Programmable Gate Array (FPGA), and/or the like (shown by way of example as medium260). Any number of computer-readable media may be used. The media may be encoded with instructions which, when executed on one or more computers or other processors, perform the process or processes described herein. Such media may be considered articles of manufacture or machines, and may be transportable from one machine to another.

As further shown inFIG.2, the memory230“includes,” i.e., realizes by execution of software instructions, an example polar scope application240, which corresponds to the application described above. The application240includes a graphical user interface (GUI)242, back-end code244, the above-described database (246), and an optional ASCOM (Astronomy Common Object Model) interface248. The application240may also include the above-described RA pixel coordinate (250), which may be associated with a particular mount102. In an example, the RA pixel coordinate250is an X-Y coordinate pair, i.e., {XRA, YRA}, which corresponds to the location of a particular pixel in the pixel array of the electronic polar scope160.

The GUI242is configured to interface with users and to display images, symbols, and various data. The back end244is configured to orchestrate user activities and to perform image processing, such as noise reduction, dark frame correction, plate solving, and the like. The database246stores coordinates of stars in the vicinity of the celestial poles. It also stores coordinates of the celestial pole (or poles) relative to those star coordinates. The ASCOM interface248is an optional component, which enables communication with optional ASCOM software and/or hardware.

FIGS.3A and3Bshow various views of the electronic polar scope160. As shown inFIG.3A, the polar scope160includes a barrel310coupled to or integral with a focal housing320. A lens312is disposed near a far end of the barrel310. Although the lens312is shown as a simple double-convex lens, other lens types may be used, and multiple lenses may be provided. The focal housing320includes an image sensor322mounted to a substrate324, such as a printed circuit board. The image sensor322may be a semiconductor charge-coupled device (CCD) or an active pixel sensor, such as one that uses complementary metal-oxide-semiconductor (CMOS) or N-type metal-oxide-semiconductor (NNMOS, Live MOS) technologies. The image sensor322is not limited to any particular technology, however. The image sensor322may be sensitive to any wavelength range in which stars typically emit light, and such light need not be visible to the human eye.

The substrate324may further have mounted thereon a memory device326, such as a ROM, as well as other components, which are omitted for simplicity. The lens312, image sensor322, and associated electronics together form a camera. In an example, the memory device326stores device-driver software for enabling the computing device170to communicate with the camera. For instance, the computing device170is configured to install the device driver software the first time the electronic polar scope160is connected to the computing device170, e.g., in a plug-and-play (PnP) manner.

In a particular example, the camera has a field of view of 13 degrees and an angular resolution of 30 arc-seconds. The focal housing320has an external connector328, such as a mini-USB or other connector, for connecting to the cable180(FIG.1). In an example, the connector328is internally wired to the substrate324or a component thereof.

As shown inFIG.3B, the image sensor322is placed at a focal plane of the lens312, i.e., light from distant objects comes to a focus at the lens-facing surface of the image sensor322. The electronic polar scope160has a central axis330. Owing to misalignments within the electronic polar scope160and/or the mount102, the center line330typically does not intersect perfectly with the RA axis110of the mount102. As a result, the center pixel of the image sensor322is typically misaligned with the center of rotation of the RA axis110. Thus, if the mount102were rotated in RA only, the imaged stars would appear to follow arcs that are not centered on the center pixel. Rather, such arcs would be centered on the RA pixel coordinate250, which corresponds to a particular pixel in the image sensor322.

FIG.3Cshows an example screen shot350as rendered on the display172by the application240. Here, the application240displays the entire field of view of the electronic polar scope160, e.g., with each pixel of the image sensor322rendered in a corresponding location on the display172. The pixel at coordinate {XRA, YRA} is the RA pixel coordinate250, which may be referenced to an X-Y origin360of the image sensor322. As the mount102is rotated in RA, any displayed stars appear to follow arcs that are centered on the RA pixel coordinate250. The application240identifies the RA pixel coordinate using an easily visualized symbol370b(e.g., a cross).

FIGS.4A and4Bshow example star images402as acquired by the electronic polar scope160and rendered by the application240on the display172. The star images402as shown display portions of the constellation Ursa Minor, i.e., the Little Dipper. By performing plate solving or other image processing on frames of the star images402, the application240determines a location410, relative to the star images, of the North Celestial Pole, As shown inFIG.4B, the application240displays a symbol370a,such as a round dot, at the determined location410. To achieve accurate polar alignment, the user may adjust the mount102(via adjustments152) to line up the symbol370awith the symbol370b.As symbols370aand370bcome to within a threshold angular distance of each other, the application240may switch automatically to a higher magnification (zoomed-in) view.

FIGS.5A and5Bshow example images510of the zoomed-in view. InFIG.5A, the two symbols370aand370bare close to being aligned and no stars are visible. InFIG.5B, the symbols are perfectly aligned, or nearly so. At this point, the mount102is accurately polar aligned, as the celestial pole intersects with the RA axis110. The mount102can thereafter achieve accurate compensation for the Earth's rotation, tracking celestial objects with minimal correction and supporting long-exposure astrophotography.

FIG.6shows an example method600that may be carried out in connection with the environment100. The method600is typically performed, for example, by the software constructs described in connection withFIG.2, which reside in the memory230of the computing device170and are run by the processor(s)220. The various acts of method600may be ordered in any suitable way. Accordingly, embodiments may be constructed in which acts are performed in orders different from that illustrated, which may include performing some acts simultaneously.

At610, the application240directs the user to cover the lens312of the electronic polar scope160, e.g., by placing a cap over the aperture162or by otherwise covering the lens312.

At612, the application140directs the electronic polar scope160to take a set of dark frames with the lens312covered. In an example, the electronic polar scope160acquires multiple dark frames and performs averaging over the dark frames for each pixel individually, thus producing an average dark value for each pixel in the image sensor322. The application240may save the pixel averages in memory130for later use. The application240may also analyze the dark frames for dead or stuck pixels, i.e., pixels that produce zero output or output that does not change from one frame to the next. The application240may store the dead and/or stuck pixel locations in a data structure for later reference.

At614, the application240acquires star images402with the mount102pointed roughly in the direction of the celestial pole. In some examples, the application240corrects the star images402based on the dark frames, e.g., by subtracting, pixel-for-pixel, the average dark value of each pixel from the corresponding pixel value in the star images402. The application240may render the star images402on the display172.

At616, the application240may accept input from the user that specifies exclusion zones in the imaged field of view. Exclusion zones are displayed areas that the user wishes to exclude from plate solving or other image processing. In an example, the user defines any desired exclusion regions by operating the GUI242, e.g., by using a mouse or other pointer to draw the exclusion region as a rectangle or other shape on the display172. The exclusion zones may include occluded areas of the sky, which are blocked by buildings, trees, or the like. They may also include objects that produce light or reflect ambient light, such as shimmering leaves on trees. The user may wish to exclude these regions to prevent plate solving from misinterpreting occluded areas as absent stars, or from misinterpreting produced light or shimmering objects as present stars.

At620, the application240generates a set of coordinates of the celestial pole (north or south) from the acquired star images, e.g., by using plate solving or other image processing to identify at least four stars in the field of view and calculating the location410of the celestial pole relative to the identified stars. In performing the plate solving or other image processing, the application240ignores any user-defined exclusion regions, thus avoiding errors associated with missing or false star images. The application240may also ignore any dead or stuck pixels.

At630, the application240displays the symbol370aof the determined celestial pole410(FIG.4B). The application240also displays the symbol370bof the RA pixel coordinate250. The symbols370aand370bare preferably superimposed over the star images402, so that the user may see both the stars and the symbols together. Displaying images of the stars is not strictly required, however, as the user merely needs to see the symbols370aand370bto perform polar alignment.

At640, the application240tests whether the symbols are close together, e.g., whether they are within a threshold angular distance of each other. If not, operation proceeds to644, whereupon the application240continues to apply a normal, un-zoomed view. At660, the user is allowed to adjust the mount102(e.g., via adjustments152). At670, the application240acquires new star images402and corrects them for dark values. Operation then returns to620, whereupon an updated pole location410is determined and the symbols370aand370bare displayed over the newly acquired star images402. Operation may continue in this loop620,630,640,644,660, and670indefinitely.

If, upon any iteration of the loop, however, the test640determines that the symbols370aand370bare separated by less than the threshold angular distance, then operation proceeds to642, whereupon the application240applies a magnified (zoomed-in) view of the symbols370aand370b.

At650, the application240(or the user) tests whether the symbols370aand370bare aligned. For example, the application240may determine that the pixel locations of the symbols370aand370bare the same, or are within some predetermined error band, and may provide an indication that polar alignment is complete, e.g., by displaying “SUCCESS!,” by sounding a tone, or by providing some other alert,. Alternatively, the user may simply decide, based on the apparent perfect or near-perfect alignment of the symbols, that polar alignment is complete, and at680the method600ends.

If, however, the symbols370aand370bare not aligned at650, then operation proceeds instead to660, whereupon the user is allowed to adjust the mount102, and then to670, whereupon new star images402are acquired and corrected. Operation then returns to620, where updated coordinates410of the celestial pole are determined and the symbols370aand370bare displayed over the new star images. This loop620,630,640,642,650,660, and670may proceed indefinitely, until the user aligns the symbols at650or decides that the imperfect alignment is good enough. Then, operation ends at680.

If, after the application240has switched to the zoomed view, the user moves the mount102too far or in a wrong direction, such that the symbols370aand370bare no longer separated by less than the threshold angular distance, then the application240may switch back to the normal (un-zoomed) view. The application240may thus switch back and forth between zoomed and un-zoomed views based on the user's adjustments. In an example, decision640is made on a per-frame basis, such that the application240may provide zoomed or un-zoomed views based on each frame. Other examples provide averaging or hysteresis, so that the views do not chatter back and forth near the threshold. When using hysteresis, the application240may apply a smaller threshold when switching from un-zoomed to zoomed display than when switching from zoomed to un-zoomed display.

FIGS.7A-7Cshow an example arrangement for defining and applying exclusion regions, such as those described in connection with acts616and620ofFIG.6.FIG.7Ashows an example un-zoomed view through the electronic polar scope160, e.g., as viewed on the display172. It can be seen that a tree710is blocking part of the field of view. Also, a leaf on the tree710is reflecting ambient light to produce a false star image720. It is also noted that the celestial pole is behind the tree710and cannot be directly seen, although its location is within the field of view of the electronic polar scope160.

As shown inFIG.7B, the user can operate the GUI242to draw a shape, such as a rectangle, over the displayed field of view to define a desired exclusion region750. Here, the exclusion region750covers the entire tree710, including the false star image720, and also covers the celestial pole location. Plate solving or other image processing can still proceed, however, as at least four stars are clearly imaged. The coordinates410of the celestial pole can thus be located, the symbols370aand370bcan both be displayed, and polar alignment may proceed as described in connection withFIG.6.

As shown inFIG.7C, a method700is provided for defining and applying exclusion regions. At770, the application240accepts user input that specifies one or more exclusion regions750. The exclusion region(s)750may be defined as one or more shapes, such as rectangles. The shapes need not be contiguous.

At780, the application240masks out the exclusion region(s) from plate solving or other image processing, e.g., by specifying that the pixels in the exclusion region(s)750are don't-care pixels which should be ignored when identifying stars.

At790, the application240performs the plate solving or other image processing, ignoring the don't-care pixels and working only with the stars found in the non-excluded regions. The pole location410is determined, and the symbol370ais displayed.

FIGS.8A-8Cshow an example arrangement for locating the RA pixel coordinate250. Location of the RA pixel250may be desired in the event that the manufacture provides no RA pixel coordinate250or when a provided location becomes invalid, e.g., following repairs or replacement of the mount102and/or the electronic polar scope160.

The depicted arrangement ofFIGS.8A-8Cbuilds upon a well-known, prior-art approach whereby the RA center of a polar scope for a telescope mount is inferred as the center of rotation of stars or other objects as viewed through the polar scope when the telescope mount is rotated about its RA axis. An alignment approach of this type is described, for example, by Celestron® of Torrance, Calif., at pp. 1-2 of a user manual for the Polar Axis Finderscope-CG-4 & CG-5 -#94223/94224. The contents and teachings of this manual are incorporated herein by reference in their entirety. As described in the manual, a user can locate the RA center of a polar scope by rotating the telescope mount in right-ascension and observing that the star or object being viewed describes a semi-circular path centered on the RA axis. The user is directed to adjust the angle of the polar scope using adjustment screws until the star or other object remains stationary in response to rotation of the mount in right ascension.

The arrangement ofFIGS.8A-8Coperates on the same principle, except that no physical adjustments are needed. Rather, the user points the RA axis110of the mount102toward a star or other object, such as a street lamp (FIG.8A). The user rotates the mount102about the RA axis110. As the mount102rotates, the stars or other objects visible in the field of view of the electronic polar scope160describe arcs810. As shown inFIG.8C, each of the arcs810describes a sector of a circle whose center corresponds to the RA axis110. In particular, each arc810describes a respective set of radii820, and the intersection of the radii820marks the spot where the RA pixel coordinate250should be placed. Just as the Celestron® approach asks the user to infer a center of the described semicircles, so too can the approach ofFIGS.8A-8Cask the user to infer a similar center of the arcs810. For example, the application240displays the radii820, or some subset of them, and the user selects the intersection point by clicking the point where the radii come together on the screen172. In some examples, the application240shows a magnified view of the area of intersection, allowing the user to accurately determine and place the RA pixel coordinate250. In some examples, the user can rotate the mount102in RA while the application240displays a magnified view of the intersection point, and the user may refine the determination of the RA pixel coordinate250until the intersection point remains stationary under rotation. Of course, the arrangement ofFIGS.8A-8Cmay be automated, as well, with the application240automatically calculating the intersection point and assigning that point to the RA pixel coordinate250.

In some examples, determination of the RA pixel coordinate250involves rotating the electronic polar scope160in its housing, rather than rotating the mount102about its RA axis110. Rotation of the electronic polar scope160in its housing may be the preferred method, particularly in cases where the housing is accurately aligned with the RA axis110by design, such that the only significant errors causing the RA pixel coordinate250to be off-center arise within the electronic polar scope160itself. To use this approach, the user points the RA axis110toward a star or other object and rotates the electronic polar scope160in its housing. Such rotation causes the star or other object to describe arcs810, from which the RA pixel coordinate250may be determined as the point of intersection of the radii820. One should appreciate that the described approach for locating the RA pixel coordinate250does not require the RA axis110to be pointed in the direction of a pole. Rather, the RA axis110may be pointed to any star or other stationary object.

Determination of the RA pixel coordinate250using this approach may be automatic, semi-automatic, or manual. According to a fully automatic approach, the mount102includes a motor (not shown) for rotating the electronic polar scope160in its housing. In response to a simple user command, the application240may direct the motor to rotate the electronic polar scope160as the electronic polar scope160acquires images, from which the application240automatically calculates the RA pixel coordinate250.

FIGS.9A and9Bshow various mechanical arrangements for mounting the electronic polar scope160. As shown inFIG.9A, the electronic polar scope160is mounted to a sky-facing side910of a mount102a,such that the lens312of the electronic polar scope160faces out. The arrangement ofFIG.9Amay be useful in mounts that are not light-tight or do not provide an unobstructed view along the RA axis110. In this arrangement, the connector328(FIG.3) may be mounted to the back of the electronic polar scope160(rather than to its side, as shown inFIG.3A) and an internal cable930may extend to another connector940on a ground-facing side920of the mount102a. The cable180may then connect to the connector940.

As shown inFIG.9B, the electronic polar scope160is mounted to a ground-facing side920of a mount102b,such that the lens312of the electronic polar scope160faces in—toward the aperture162. The arrangement ofFIG.9Bis thus similar to the one shown inFIG.1. The electronic polar scope160may be placed in a housing950. In some examples, the housing950also serves as a light baffle, preventing stray light that enters the mount102bfrom reaching the lens312.

An improved technique has been described for performing polar alignment of a mount102of a telescope or other astronomical instrument. The technique includes acquiring star images402from an electronic polar scope160and determining a location410of a celestial pole relative to the star images402based on computerized matching of the star images402to information in a database246. The mount102has a right-ascension (RA) axis110, and the technique directs an adjustment to the mount102so as to align the determined location410of the celestial pole with a location of the RA axis110.

Having described certain embodiments, numerous alternative embodiments or variations can be made. For example, although embodiments have been shown and described in connection with fully-functional equatorial mounts102,102a,and102b, embodiments may also be provided that use other types of mounts adapted for equatorial tracking. For example, embodiments may be used with an altazimuth mount equipped with an equatorial wedge, or with a star tracking mount, such as the SkyTracker and SkyTracker Pro camera mounts, available from iOptron Corporation of Woburn, Mass. Such star tracking mounts may include holes or housings for receiving the electronic polar scope160. The electronic polar scope160may be rotated easily within the holes or housings to locate the RA pixel coordinate250, if necessary, and polar alignment can proceed in the manner described above.

Further, embodiments have been described in which adjustments152of the mount102are provided in the form of manual knobs. In other embodiments, however, the functions of the knobs may be replaced with motors. The motors may operate under control of the application240, which may automatically vary the adjustments152to polar align the mount102with little or no user interaction.

Further, although features have been shown and described with reference to particular embodiments hereof, such features may be included and hereby are included in any of the disclosed embodiments and their variants. Thus, it is understood that features disclosed in connection with any embodiment are included in any other embodiment.

As used throughout this document, the words “comprising,” “including,” “containing,” and “having” are intended to set forth certain items, steps, elements, or aspects of something in an open-ended fashion. Also, as used herein and unless a specific statement is made to the contrary, the word “set” means one or more of something. This is the case regardless of whether the phrase “set of” is followed by a singular or plural object and regardless of whether it is conjugated with a singular or plural verb. Further, although ordinal expressions, such as “first,” “second,” “third,” and so on, may be used as adjectives herein, such ordinal expressions are used for identification purposes and, unless specifically indicated, are not intended to imply any ordering or sequence. Thus, for example, a “second” event may take place before or after a “first event,” or even if no first event ever occurs. In addition, an identification herein of a particular element, feature, or act as being a “first” such element, feature, or act should not be construed as requiring that there must also be a “second” or other such element, feature or act. Rather, the “first” item may be the only one. Also, the terms “based on” and “based upon” should be interpreted as meaning “based at least in part on” or “based at least in part upon,” as bases need not be exclusive unless explicitly stated. Although certain embodiments are disclosed herein, it is understood that these are provided by way of example only and should not be construed as limiting.