One of the powerful abilities of Superman is his ability to make several layers of opaque solid objects translucent to him and only him alone. What plausible future technology would allow us to see through animate and inanimate objects without destroying them or giving them cancer? What existing technology do we have that is closest to this? Is such technology (future or current) light enough to wear on the street?
If you will, let's start with some pseudo-biology. We see three colors because we have photoreceptor cells filled with color pigments (red, green, blue) which, when excited, send signals to our brain to be processed as information.
The visual signals that are theoretically possible are not limited to these three wavelengths of Electromagnetic radiation (called "visible light").
Birds have an additional 2 types of photoreceptors to detect ultraviolet light (for "night vision," esp. in nocturnal birds like owls), as well as another type with an unknown function, thought to possibly be related to detecting motion (backed up anecdotally by the fact that birds have an acute sense for moving prey, and there is a clear evolutionary advantage to this ability)
anyways, what other similar signals are there just floating around for super-heros to sense using their unique biologies?
Infrared (see: snake vision), and for the more fantastical among us: background radiation, radio waves, x-ray radiation....
Without backing this up with science, I would say that in a tiny biological receptor such as an eye, it would be easier to detect shorter wavelengths (i.e. x-rays) than longer wavelengths (microwave radiation, radio waves). More energy=easier to excite a specific receptor molecule.
Don't let hard science ruin your dreams, base it in plausibility, and write the story! We'll suspend our disbelief.
edit: to address seeing through walls in particular.... high energy, low wavelength radiation (X-ray radiation, etc.) is NOT GOOD at passing through walls. microwave and radio radiation are MUCH BETTER at achieving this, due precisely to the fact that their longer wavelength puts them well out of range of exciting electrons in the matter within walls etc. (but also within our imaginary photoreceptors!)
edit2: Read here for some basics on how radio waves are turned into useful signals: https://www.explainthatstuff.com/antennas.html
If you want this ability to be an inborn ability (which makes sense if taking the unique photoreceptor route), then sticking a metal antenna up through the jaw and into the back of the eye seems like it's just going to hurt, and now allow our superman to see radio waves through walls. But you could handwave and say he evolved a rigid antenna like structure like that can also conduct electricity and then that allowed his species to evolved radio-wave vision.
Anyways, good luck! And if history has proven anything, its that superpowers dont need to make sense anyways!
The only thing I know that has the power to do that today is machine learning, meaning by doing an excellent prediction. You could make an analogy between deep learning and high sensitivity. Deep learning prediction is based on learning from slight variation in data in a very complexe way. The ability to make several layers of opaque solid objects translucent to him is emerging from the hability of Superman's brain to process the data coming from his super hearing and vision.
A more technical approach would be to have some sort of camera with higly sensitive resolution (audio and video). It would be associated with back end processes made of deep learning rendering user friendly restitution of different possible layers. The restitution could be some text or visual representation of the different layers, depending on how this technology is advanced.
Backscatter X-ray as used by the TSA is the best answer I can think of, though I don't really know enough about it to say much as far as how much this could be extended in terms of accuracy.
Really the problem is that any kind of EM radiation that is capable of penetrating objects is also highly dangerous, because the higher frequencies that allow one to see through objects are also those with higher energy that thus do more damage.