I've been thinking about this a lot lately (therefore this may be excruciatingly long), so here are my thoughts as a science grad student and fellow psychonaut:

As a sort of preface, science begins with an observation to which a hypothesis is formed and tested. It's interesting to consider if we're actually able to 'observe' our own consciousness to the degree that we can test it. I think if we were able to, we would already have a definition for it. There's an interesting TED talk that outlines three plausible theories, but they largely remain abstract. And when studying something abstract, it takes an equivalent tool (human language, arbitrary rating system, etc.) to 'measure' it. In this sense, our scientific understanding is not at a level that allows us to measure consciousness, just formulate new hypothesis as to what it could be.

I frequently study and do some research on molecular evolution. It seems like we attribute consciousness to being an artifact of human existence, but I strongly disagree. It just does not seem like if I were to take two bins, one with the most simplistic bacterium and the other with the human being, that all of the other organisms on the planet would fall into the bin with the bacterium. I think there is some continuum of consciousness, but this is again limited to how we explain it. In the evolutionary sense, I think my idea makes sense. Consciousness being an artifact of human existence would imply some genetic 'switch' was made that is solely responsible for our intellect relative to our ancestors. And if it were that simple, geneticists would already hold the key with recent genomic developments. There are some studies that I haven't looked into that may interest someone, where they are looking to see if animals (particularly pets) actually have some sort of memory. Everyone I mentioned this to says, "of course they do!," but I feel that it supports my idea and demonstrates that consciousness may be multifaceted.

To get on topic, I recently had the opportunity to visit a medical research facility where one of the labs were extremely thinly slicing human brains up for study. I won't get into the details, but the scientists were looking at the molecular patterns within the brain. This might suggest that this consciousness, the thing that makes us, us, is simply an intricate biochemical 'dance'. In this sense, the measurements you seek to make may simply be far out of scope of the tools available today. And if levels of consciousness is truly composed of varying degrees of memory, 'computation potential?', etc., it will take the whole molecular 'picture' of the brain at any moment to understand how it's working. Also, in respect to my continuum idea, it might be best to understand what causes the difference in consciousness from organism X to the human being, which is where I think studies will mainly be heading.

Of course this answer is incredibly boring and 99% of the details aren't there to uncomplicate the matter, so here is an idea I have that I'd love to do:

The 'higher consciousness' induced by deep meditation, psychedelics, etc. also set up a new condition in the human mind. Scientists always seek to compare condition X to Y and find the largest variable to explain whatever phenomenon of study. I think these states provide a good opportunity to simply find some things that change, although what's happening as the result of these states requires the understanding first.

I wanted to try and get some crowd-funded support (obviously broke in school) or get a team going to do some high resolution brain wave studies. The enabling factor of the project would be an open source brain-computer interface. It would be pretty fun, and likely valuable, to set up a highly controlled span of different activities that use the mind in different ways/degrees and measure the brain patterns during these times. Then, after developing profiles for these activities, try and do the same things on different substances evoking this 'higher consciousness.' MATLAB has tools that can analyze and do comparisons with the data, which would be ridiculously neat. I think it would be interesting to see if any of these meditative, psychedelic, etc. states relate to each other. I'd love to elaborate, but no one has time for that. This is just about the only affordable tool I can imagine to do this today.

Hope some of this is valuable.