Why didn't the Imperial fleet detect the Millennium Falcon on the back of the star destroyer?

Question

Han Solo fools the Imperial Navy by clamping onto the back of one of the star destroyers just when they thought the Millennium Falcon jumped to hyperspeed.

Why didn't the Imperial Navy detect a ship clamped on the back of one of their own?

At least 3 Star Destroyers and multiple TIE fighters chased the Millennium Falcon through the asteroid field. Each of those ships probably had several radar, lidar, and optical sensors (or whatever sensors they use in the Imperial Navy) to track every movement of the Millennium Falcon. With numerous sensors on multiple vehicles watching it, the Falcon couldn't just hide on the back of a ship. At least one ship should have seen it.

Answer 1

There appears to be six elements to Han's plan that prevent the detection of the Falcon by the fleet.

1. The ship is shut down and not emitting any electromagnetic radiation that might give them away.

Inside the Falcon’s cockpit all was quiet. Han Solo had stopped his ship and shut down all systems so quickly that even the customarily talkative See Threepio was silent. Threepio stood, not moving a rivet, a look of wonder frozen on his golden face.

_{^{Empire Strikes Back: Official novelisation}}

2. The ship is parked directly behind the main (forward-looking) radar tower.

The Millennium Falcon perches on the back of former-Captain Needa’s Star Destroyer, just behind its main radar tower—too close to be seen. They say “Keep your friends close, and your enemies closer.” Han Solo is demonstrating the truth of that adage in the extreme

_{^{The Empire Strikes Back: So You Want to Be a Jedi?}}

3. The ship is invisible to the fleet's scanners, possibly hidden by the bulk of the Star Destroyer

“Well, there’s no trace of them, sir, no matter how they did it,” the tracking officer replied, still unable to locate the Millennium Falcon on his viewers. “The only logical explanation is that they went into light-speed.”

...

The Dark Lord turned, and Admiral Piett and two of his captains came to report their findings. “Lord Vader,” Piett said, “our ships have completed their scan of the area and found nothing. The Millennium Falcon definitely went into light-speed. It’s probably somewhere on the other side of the galaxy by now.”

4. The ship physically blends in with the colour of the Star Destroyer.

But even if anyone had looked directly at the port aft of Avenger’s command tower, they might not have immediately spotted the Millennium Falcon, which rested flat against the destroyer’s hull, right where Han Solo had landed it. Because of the Falcon’s faded white exterior, the Corellian transport blended right in with the Imperial ship.

_{^{Empire Strikes Back: Junior novelisation}}

5. The crew of the Star Destroyer were too busy notice that the windows were blocked by the bulk of the Falcon.

The Millennium Falcon’s possible destination routes were quickly computed by the Imperials. As the Executor and Star Destroyers prepared to leave the area, every Imperial helmsman, navigator, controller, and technician kept their keen eyes on their consoles and monitors. And because all sensors had already indicated the Falcon had vanished from the sector, not one Imperial soldier thought to look out a window.

_{^{Empire Strikes Back: Junior novelisation}}

6. The one crew member that did notice decided not to report it in order to make a deal with Boba Fett to split the bounty. He was subsequently unable to report it.

Ashon switched on the relay screen, seeing what the droid was seeing. Sure, he could leave the repairs to the droid’s own protocols, but he still had his pride. He’d been head of engineering once. He knew every millimeter of the—
“Hold up. Pan ninety left.”
What was that? A landing claw?
Something had parked itself on the back of the Avenger.
Definitely not Sienar. The design looked Corellian.
A YT-1300 transport.

_{^{Star Wars: From a Certain Point of View - Standard Imperial Procedure}}

Answer 2

Supplementary answer (to a comment by @Loren Pechtel, but relevant overall):

Actually, both sonar and radar detect more than just the cross-section of the target — they detect the difference in range over the cross-section of their angular resolution, which is precisely how one can use side-scan sonar to map a river bottom in one pass.

However, it is true that even this wouldn't help with spotting the ship much in this situation, for two reasons:

1. The "background" is already extremely cluttered and would be prone to sending back multiple reflections from a huge number of points for a single scan pulse; it would look like a "cloud" of reflections with a strong front surface but a non-trivial "depth" with all of the additional scattering. On top of that, the MF isn't tall enough to actually be that much different from the true / expected surface, and from many angles would be partially obscured by the other superstructure of the star destroyer, rendering it even harder to spot.
2. When trying to find something "in general", they would be using the broadest aperture settings on their scanners in order to sweep as much area as possible as quickly as possible; this makes it much harder, potentially completely impossible, to distinguish the Falcon from the star destroyer itself. This is the same distinction found between current "acquisition" and "tracking" radars, and is a fundamental property of how any "ping response" scanner pretty much has to work, so it is perfectly plausible that it would still apply at the Empire's technology level.

Answer 3

First off, it's just a clever hiding spot. The colors of the ship match and seeing star destroyers weren't completely smooth it would be hard to see something as irregular.(Also the ship isn't covered in windows, and you would probably not have many people looking outside with their bare eyes...instead they would rely solely on their equipment)

Second, take a close look at the radar screens in the movies (and especially the games). The displays seems to be heavily inspired by Sonar screens. Assuming they work similarly they would only be able to detect the size/shape of a vessel. but if such a relatively small ship is literally attached to a massive ship like a Star Destroyer it would probably be seen as a part of the ship. Any irregularities would probably be brushed off as malfunctioning equipment and be ignored because who would be crazy enough to land on a star destroyer?