Where are the Food Deserts?

A food desert is an area where healthy food options are out of reach. You know if you're in one, but it's surprisingly difficult for the Ivory Tower crowd (like me) to figure it out. For one thing, there are at least three components in that definition. What's "healthy"? What's "out of reach"? And even what's an "area"?
When I first started thinking about this, I figured, well, you just measure the distance from where a person lives to the nearest supermarket.

image from Data Underload, flowingdata.com

Turns out, that's a lousy definition. Makes for pretty pictures, though, like the one on the right, from Nathan Yau FlowingData.com (love your site by the way, Nathan).
The main problem with this approach it doesn't take account of of social space. Using this approach, the biggest food deserts are in actual deserts. Which would be fine if you were plopped down in a random part of the country each morning and had to figure out how to eat from scratch every morning.
But we tend to live, work, play, and "get by" in neighborhoods, neighborhoods that are highly structured in physical space in a way that reflects social relations.

When we looked for food deserts in Alameda county, we found that the "deserts" lay beyond the toney hills, in the outlying commuter suburbs, and the places we expected to see low food availability appeared to be chock-a-block full of supermarkets. Geographic space is part of the food desert picture, but somehow we need to get the idea of social distance in there as well to get at the idea of "out of reach".
And then, there's also the idea of "healthy" food. A supermarket may be short-hand for the availability of affordable healthy food options, but there are plenty of supermarkets whose produce aisle looks like the set for a horror movie, and there are also corner stores with gourmet appeal.
At the APHA meeting, I saw a bunch of posters where people had put a lot of work into figuring out food deserts in their communities, including a very ambitious project to describe food availability in great detail in New Orleans.
But I want to come up with a definition of a "food desert" that I can apply across the country, and without having to visit every supermarket, corner store and farmer's market. Lately, I've been thinking about coming up with some sort of relative distance measure, like the distance to the nearest supermarket, divided by the distance to the nearest outlet that sells tobacco or alcohol. So far, I've downloaded all the supermarket locations across the country, but the number of places that sell tobacco is just too huge. Hmmm.

Then, there are other important aspects to the social space that defines a food desert. I've got a job, and I drive about 40 miles to get there, so in the course of my day, I come across many food shopping alternatives. But there are many places along my route that someone without a car would have a great deal of difficulty getting to decent food. I can walk into any food vendor and get great service, even while wearing a hoodie. But not everyone wearing a hoodie gets the opportunity to pay cold hard cash for food, let alone get decent helpful service in the aisles.
I'm also re-thinking food deserts as being located in a clearly delineated physical space, and instead as a condition of what an individual or family experiences. I might not be in a food desert, but my neighbor might be.