Dart is approaching Didymos B aka Dimorphus with a speed of 6.6 km/s. How many images could be taken and transmitted between Didymos B just filling the entire image and the last image just before impact?
This paper from Fletcher et.al. (2016) DRACO:DIDYMOS Reconnaissance for OpNav, provides some hints.
- page 2, second column (image capture rate)
As many images as the available down-link supports will also be sent to Earth, estimated at roughly one image every 5 s. These proximity imaging observations will provide information about the shapes of the two objects and their geologic properties.
It looks like they are trying a best-effort for these proximity imaging observations. Not surprising since time is short!
So the answer to the OP's question is: zero, perhaps one, the last one being when the target is just about filling the field of view of the DRACO camera (0.29° of FOV).
Interestingly, we learn from the paper that the camera has ~5.5 Mpixels resolution (2560x2160). Furthermore we learn that
- page 2, 1st column (image coding)
DRACO processing will have many options for reducing data volume due to limited time to return images prior to final impact with Didymos B. These include: 2x2 pixel binning, reduction to 12b data, lossless image compression algorithms, and windowing of the image.
We can conclude that, a full frame (without cropping) image is a 5.5*12 =66 Mbits file. To transmit such a quantity of information back to a Deep Space Antenna in 5 seconds requires a communication system that can reach 13.2 Mbps.
Now, those who love playing with link-budgets can reverse engineering the antenna gain embarked on DART!
Addendum 1 (integrating resource from ESA pointed by @KuteKitty_pleaseStopBarking)
A more recent powerpoint from ESA by Andy Cheng (2018) DART Mission Update gives some additional data points.
- On slide n°5, a much more accurate impact speed is given, 5.975 km/s, instead of 6.6 km/s
- On slide n°7, a bullet point reads
DRACO acquires image at 0.5m/px by 17 sec before impact ...
It is not clear whether this "17s before impact" is the programmed time for the last image acquisition. Note that 6x17=102 km and at that point the target does not fill the whole FOV. Knowing that DART has image cropping capability, we would expect that, before sending the image back it would reduce the image to only the "area of interest", perhaps something like one third of the "full frame" image (when the target fills the whole FOV). Therefore, at down-link speed (13.2 Mbps, according to our previous estimate) there would be more opportunities to capture and transmit additional images and there is no obvious reason why we would stop at 17s.
This additional discussion does not change the answer to the OP's question: "zero, or perhaps one", while the supporting arguments may differ.
Addendum 2 (Communication system parameters)
This presentation by Andy Rivkin (2020) provides us the final missing information, the down-link bit rate constraint.
The information is given at the bottom of slide n°9:
Impact down-link bitrate: 3 Mb/s.
That's 4.4x lower than my guessimate of 13.2 Mbps. Recall that I arrived at 13.2 Mbps by dividing the "full frame" size of the image (5.5 Mpixels at 12b/pixel) by the 5-second transmission time based on the (approximate) image transmission rate given in Fletcher paper. This is how I propose to explain this discrepancy:
- It could be that DART communication is designed to transmit one image every 5 seconds, but the size of the image is reduced by cropping (windowing), to retain only 1/4th of a full-frame size (the "area of interest"). In this case, the last image could be beamed back at about 35-30 km from impact.
Those who love doing link-budgets may notice that the same slide mention the size of the X-band transmit antenna and amplifier power. You can then reverse engineering which Deep Space Antenna will be used to receive this last image.
This JHU Video shows a simulation of the final 1 hour before impact with the caption:
This DART simulation video shows how the spacecraft gradually tracks and zeroes in on Dimorphos. The left display shows the information that is downlinked from the spacecraft. It’s a subset of the overall image that’s selected to contain the targeted asteroid. The full image is in the bottom right, with a yellow box highlighting the downlinked portion. Once the system identifies Dimorphos and calculates the necessary maneuvers to keep the asteroid in view, it fires the spacecraft’s thrusters, as shown in the upper-right display.
Taken from the excellent JHU interactive webpage on SMART Nav.
As stated in the caption, the spacecraft doesn't return the full image, just a subset containing the target Dimorphos at ~half/quarter resolution (1D/2D). The video seems to indicate that images are taken and returned every 2 seconds and Dimorphus fills the smaller sub-frame at about the I-10s mark and fills the full frame in the last frame before impact.