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I am in trouble calculating the ground resolution of MVIC instrument onboard New Horizons; I found several documents about MVIC specs, like this one:

http://www.boulder.swri.edu/pkb/ssr/ssr-payload-overview.pdf

I'm used at seeing FOV defined as a DEGRESSxDEGREES values, such as for LORRI, which has a 0.29°x0.29° FOV and 1024x1024 pixel sensor, but for MVIC:

Six of the arrays have 5000 (columns) x 32 (rows) [...], TDI arrays have a field of view of 5.7° x 0.037°, and the frame transfer array has a field of view of 5.7° x 0.15°

(p. 11)

My calculations do not match with this statement:

The two TDI panchromatic arrays are sized to meet the 0.5 km/pixel Group 1 mapping requirement near closest approach when Pluto’s diameter subtends ~5000 pixels.

I calculated that at closest approach (15405 km), an object 2477 km wide would subtend 5000 pixel in a 5000x5000 (?) sensor if the camera had a FOV of around 9°. So this is not the right method to calculate MVIC resolution. Which is the right method?

For LORRI my numbers are ok:

  • Size: 1024 x 1024
  • FOV: 0.29° x 0.29°
  • Diameter: 2477 km
  • Distance: 15405 km

--> Resolution: ~70 m pixel (~50 declared on page 12)

I use this page for quick calculations: http://win98.altervista.org/telescopio.html

NH should arrive as low as 3500 km from surface, which would give 17m/pixel for LORRI.

I am tracking NH here.

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A good sanity check is to compare your results with what the New Horizons team is reporting. It is also useful to consider whether there are any other factors at play that could throw the numbers off.

As a point of reference, this undated article on the New Horizons website discusses the Ultima Thule flyby and states:

The pixel sizes of the best expected color and gray scale images and infrared spectra will be 330 meters, 140 meters, and 1.8 kilometers respectively. There is a chance of higher resolution grayscale images, with 33 meter pixels, if the high-resolution LORRI camera is able to point accurately at Ultima, but the necessary accuracy isn't guaranteed


Calculated resolutions

For reference, the estimated diameter of Ultima Thule is about 30 km.
(The estimated size of Ultima Thule is discussed in more detail in this answer)

Using the calculator you linked to with a distance of 3500 km I get the following:

MVIC (color and greyscale)
Sensor width: 5000 pixels
FOV: 5.7°

Quoted maximum resolution: 330 m/pixel

Theoretical best resolution: 69.60 m/pixel
FOV at target: 348.30 km

LEISA (IR)
Sensor width: 256 pixels
FOV: 0.9°

Quoted maximum resolution: 1800 m/pixel

Theoretical best resolution: 214.65 m/pixel
FOV at target: 54.95 km

LORRI (greyscale)
Sensor width: 1024 pixels
FOV: 0.29°

Quoted maximum resolution: 140 m/pixel (high probability of imaging UT)
Quoted maximum resolution: 33 m/pixel (low probability of imaging UT)

Theoretical best resolution: 17.29 m/pixel
FOV at target: 17.71 km


Limiting factors

The calculated numbers clearly don't match those published by the New Horizons team. I see three reasons why this could happen.

  1. Blur
    Both MVIC and LEISA are pushbroom scanners and because of the low light levels at Ultima Thule they will be slewing the platform slower than they did at Pluto. This is less of an issue for LORRI since it doesn't use the pushbroom technique but it too is affected by the low light levels and thus also needs longer exposures. This could lead to increased image blur particularly since the target's position is imprecisely known (this may result in incorrect pan or slew rates). Due to their design, MVIC and LEISA are particularly affected.

  2. Field of view considerations
    Ultima Thule is a small target with an uncertain position. To improve the odds of imaging the target the field of view needs to be kept large; this reduces the ground resolution. To further improve the odds and to allow higher resolution images to be taken, multiple images will be taken in a grid pattern covering the area where Ultima Thule is likely to appear. This should allow (fairly) high ground resolution images to be taken but at the expense of taking up precious time and having a lot of blank frames. Keep in mind that capturing any image at all takes priority over a chance of taking a detailed image.

    In the case of LORRI there's an addition consideration: the imager's restricted field of view. At closest approach LORRI only has a field of view of ~18 km which is considerably smaller than Ultima Thule's estimated 30 km size. Time constraints (see below) mean that at closest approach it is impractical to do extensive grid scanning with LORRI; this decreases the odds of a non-blank image being returned. I calculated that the closest LORRI images that are expected to show Ultima Thule will be taken at a range of 14000 km (high imaging probability) and 6500 km (low imaging probability).

  3. Speed and distance
    New Horizons will be passing close (3500 km) to a small target (and considerably closer than it did Pluto). The relative speed is also high (14 km per second). The window of opportunity for imaging will be much smaller than at Pluto and slew rates and parallax shift while imaging will be higher; this will exacerbate the two aforementioned issues.


Ultima Thule imaging schedule

Ultima Thule flyby imaging schedule Source: NASA (cropped, edges cleaned up)

This is the imaging schedule as published in the press kit.

Here's a rough breakdown of this diagram with distances given in km from point of closest approach (not ranges) accurate to within about 100 km:

LEISA (IR) -65750 to -64000, -34900 to -26000
MVIC (color) -42500, -17400 to -15400, +25600 to +26850
MVIC (greyscale) -10500 to +2250, +5600 to +10300, +22200 to +23400
LORRI (greyscale) -61800 to -60000, -42400 to -42000, -31900 to -23100, -17000 to -15100, -10250 to +2500, +2800 to +4400, +5900 to +10500


Conclusions

The images taken during the encounter are to be acquired from a variety of distances under less than ideal conditions. Image quality will therefore be lower than calculations based on a stationary observer at closest approach would suggest.


Resolution during capture in meters per pixel

Resolutions shown assume perfect image capture (i.e. no blur).

Time SCET Distance Range LEISA (IR) MVIC (color) (grey) LORRI (grey)

                                     .------.                                    
-4553   04:17   -65750    65850      | 4040 |                                    
-4432   04:19   -64000    64100      | 3933 |                                    
                                     '------'                          .-----.   
-4280   04:22   -61800    61900                                        | 306 |   
-4155   04:24   -60000    60100                                        | 297 |   
                                                                       '-----'   
                                                     .-----.                     
-2943   04:44   -42500    42650                      | 849 |                     
                                                     '-----'           .-----.   
-2936   04:44   -42400    42550                                        | 210 |   
-2909   04:45   -42000    42150                                        | 208 |   
                                     .------.                          '-----'   
-2417   04:53   -34900    35100      | 2152 |                          .-----.   
-2209   04:56   -31900    32100      |      |                          | 159 |   
-1801   05:03   -26000    26250      | 1610 |                          |     |   
-1600   05:06   -23100    23350      '------'                          | 115 |   
                                                     .-----.           '-----'   
-1205   05:13   -17400    17750                      | 353 |                     
                                                     |     |           .-----.   
-1177   05:13   -17000    17350                      |     |           |  86 .   
-1066   05:15   -15400    15800                      | 314 |           |     |   
-1046   05:16   -15100    15500                      '-----'           |  77 |   
                                                             .-----.   '-----'   
 -727   05:21   -10500    11050                              | 220 |             
                                                             |     |   .-----.   
 -710   05:21   -10250    10850                              |     |   |  54 |   
    0   05:33        0     3500                              |  70 |   |  17 |   
  156   05:36     2250     4150                              |  83 |   |     |   
  173   05:36     2500     4300                              '-----'   |  21 |   
                                                                       '-----'   
                                                                       .-----.   
  194   05:36     2800     4500                                        |  22 |   
  305   05:38     4400     5600                                        |  28 |   
                                                             .-----.   '-----'   
  388   05:39     5600     6600                              | 132 |             
                                                             |     |   .-----.   
  409   05:40     5900     6850                              |     |   |  34 |   
  713   05:45    10300    10900                              | 217 |   |     |   
  727   05:45    10500    11050                              '-----'   |  55 |   
                                                             .-----.   '-----'   
 1537   05:59    22200    22450                              | 448 |             
 1620   06:00    23400    23650                              | 471 |             
                                                     .-----. '-----'             
 1773   06:03    25600    25850                      | 515 |                     
 1859   06:04    26850    27100                      | 539 |                     
                                                     '-----'                     

Values derived from distance data shown in the Imaging schedule diagram.

  • Time Seconds relative to closest approach
    Derived from distance assuming a velocity of 14.44 km per second. Negative for approach, positive for departure.
  • SCET Spacecraft Event Time on 2019-01-01
    Derived from time based on closest approach of 05:33:30 SCET. Format is hh:mm.
  • Distance Distance in km to point of closest approach
    Estimated from diagram. Negative for approach, positive for departure. Accuracy is about ±50 km.
  • Range Distance in km from spacecraft to 2014 MU69
    Derived from distance assuming a closest approach of 3500 km. Rounded.

Initial images

The images planned to be sent during the initial (daily) pre- and post-encounter transmissions are:

MVIC (color) 900 m/px (NYT 2)
LEISA (IR) 28 wavelengths at 1800 m/px (NYT 3)
LORRI (greyscale) 8000 m/px (Failsafe 1), 5000 m/px (Failsafe 2), 300 m/px (NYT 1), 140 m/px (NYT 2, low probability), 140 m/px (NYT 3, different image, low probability)

These will presumably be lossy-compressed images with lossless ones being transmitted later.


Sources


I hope that's helpful. I'll go over it again in a bit and see if I can improve it.

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