Are some sources of electromagnetic radiation theoretically (or perhaps technically!) more challenging to detect than others? In a previous question, I learned that in order to detect an object in space, what matters is how much electromagnetic radiation it is giving off, and what sources of EM radiation the sensor can pick up. 
Given that the sensitivity of the sensor over the spectrum is a parameter for detectability, I would like to learn if some wavelengths of EM radiation are more difficult to detect than others, over increasingly longer distances in space.
From my experience in biology, I know that longer wavelengths of lights from a source can be "pierce" deeper into tissue than shorter wavelengths (a bit counter-intuitive!). In fact, that's the premise of "two-photon microscopy" -- using wavelengths of light with such low energy that fluorescent dyes need to absorb two low energy photons in order to be excited. So, the probability of that happening is lower, but there are many benefits, including the fact that longer wavelength light can penetrate deeper into tissue.
Does the physics behind such concerns at the microscale also affect detectability at astronomical scales? Is some EM radiation easier to detect than EM radiation with other energies? Can EM radiation of certain energies "travel" longer distances through imperfect, real space?
 A: High-energy radiation tends to get randomly deflected rather than slowed down by a medium, making lenses impossible. It also will bounce off of individual atoms of a mirror unless it hits at a very steep angle, so mirrors are difficult. Diffraction gratings won't work because you can't make slits smaller than the atomic scale. In the worst cases, even a pinhole camera won't work well since enough radiation that misses the hole will get through to blur the image.
If you just want to detect it's not a problem, but if you want to see the direction it will be more difficult.
I'm not an expert though, so I might be missing something. Is there another method that works well?
A: Let's jointly go through the motions of calculating our signal strength in detecting electromagnetic radiation from an object in space. This means starting at the emitter and going through the relevant steps until the light/radiation reaches our detector:


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*Emission. Only if the source emits (appreciably) at a particular wavelengths and towards you, there is even a chance for you to detect it. High-energy radiation can be highly directed, e.g. in quasars. That can be a blessing: If you happen to be inside the beam, you receive more of the energy than you would if the same radiation were distributed in all directions. If you were to use the language radio engineers use, such as source has a high antenna gain (a gain compared to uniformly radiating in all directions).

*Absorption and scatter. The space between you and the source can contain matter, including (neutral) gas clouds, plasma (charged gases that tend to be overall neutral), and dust. There are too many detail effects for me to have confidence in giving a comprehensive overview. But you certainly already know of evidence of a few: In the visible wavelength range, a typical trend is that short wavelengths get scattered more by gases and especially small sub-wavelength sized dust particles, which is why the rising or setting sun looks redder and near-infrared light lets us peek a bit closer towards the dense central region of the galaxy than visible light. Mid-IR and far IR has problems with gas (and other molecules) because they have lots of rotational and vibrational spectral lines, absorbing and scattering a lot. Radio waves may not penetrate through plasma clouds, depending on wavelength, charge density and composition. On the other, energetic, side of the spectrum you first have X-rays. At a certain energy range, they can be better at penetrating some matter, much like you know from medical x-rays. Finally, not even by looking in a direction of relatively empty space can you hope to avoid all of these effects: The atmosphere, which includes a plasma cloud known as ionosphere, will always be in the way (unless you put your observatory into space, which is done for some spectral regions). Astronomers call the different spectral regions where the atmosphere is reasonably transparent for electromagnetic radiation "windows."

*Distance. The emitted radiation, however focussed it may (or may not) be, will dillute into a larger cross section as it propagates, diminishing in intensity (power per area) as $1/d^2$ with distance $d$ because $d^2$ is how areas (e.g. the cross section) grow geometrically. If the space is empty (and we covered all other effects above), this is the same for all wavelengths. Yet it means that minor differences matter slightly less than it may seem: A detection efficiency that is diminished by a factor of 1000 only leads to ca. 30 times reduction in distances if all else is equal (but that corresponds to ca. 30000 times less visible volume).

*Detector. Your detector will only ever pick up a fraction (<= 1.0) of the electromagnetic radiation that arrives at it. We have some superb detectors for some wavelengths, for example single-photon detectors with detection efficiencies >70% for visible light, and there are nearly perfect mirrors that can focus light from only a particular direction onto the detector (and adaptive optic technology to do this better than atmospheric scattering would otherwise allow by undoing much of it!). For other spectral areas, we have hardly any detectors worth noting. For example, for the THz spectral region (also known as millimeter waves) that lies between visible light and radio waves, there is hardly anything but bolometric detection, measuring the change in temperature caused by this radiation. That is very inefficient because enough photons must be collected to cause a measurable change in temperature, which even for cryogenically cooled microengineered detectors is tricky. Additionally, good focussing can become a challenge. For radio waves, due to the long wavelengths, the only chance to get good focussing is to build large dish-shaped reflectors, and the engineering (or perhaps funding constraints) usually becomes prohibitive at a few hundred meters diameter. For gamma rays, "optics" become especially challenging and fail to give anything near the extreme performance you might hope for based on the short wavelengths. In fact, gamma rays produced in lightning (a weather phenomenon in earth's lower atmosphere) are detected by space-based x-ray/gamma "telescopes" just as the cosmic gamma ray bursts they were designed to be looking for.

*Noise. Other sources of the electromagnetic radiation you are looking for can make it impossible to see a small signal. This is especially problematic with radio and millimeter waves because even just the environmental heat will cause fluctuations in your receiver's electronics that look like a signal but are only thermodynamic noise. It is no coincidence that the cosmic microwave background radiation was only discovered (accidentally) when radio-receivers were cooled to truly cryoscopic temperatures! In addition to this thermodynamic noise, you also get technical noise. The most obvious source, apart from technical limitations of your detector, are earthly signals picked up by you. The glow, or light pollution, of a city is a prime example and exists in other spectral regions in a similar fashion.
To sum up: It's complicated!
A: A partial answer could show you that the Earth's atmosphere is actually a big obstacle for a large range of radiation, starting from UV light to shorter wavelengths. X-ray astronomy is largely impossible on Earth, which is why such telescopes are always located in space. Long wave radio signals however can be picked up also through the atmosphere, air is "see-through" for such frequencies.
Absorption of electromagnetic radiation in a medium always plays a role, especially in dense matter such as solid insulators, organic tissues or gases. However, since the density of such materials in outer space is extremely low, hardly any light is absorbed along its way to the observer. The effect is there in principle, but it is greater by orders of magnitude in actual matter. Gamma ray astronomy for example is certainly possible, pulsars and black holes have been detected using this technology in the recent years, such as this:

A much greater problem is to my knowledge angular resolution; two stellar "disks" cannot be resolved arbitrarily close. Instead, there is a classically minimum distance they can be separated from each other before they merge into one disk. Also, the intensity of very distant stars can decrease so much that it becomes hard to detect those few photons that reach the detector, among with other technical difficulties such as stabilization or accounting for changes in air density (for
Earth-based astronomy). The Hubble Deep Field for example was recorded with visible and UV light, which has travelled across the whole observable universe (~12 billion light years).
