A click, a whirr, and a faint chemical smell as you waved the stiff piece of plastic-coated paper back and forth and watched an image emerge from a cloudy blur: In our age of always-on camera phones, it’s hard to describe just how magical instant photography used to be.

So for anyone who remembers what taking pictures was like before the advent of digital photography, the Ogden’s new “Self Processing: Instant Photography” show will have a certain degree of nostalgia value.

But the show isn’t just an opportunity to look at a once common but outmoded way of making images. With a canny eye for works that took advantage of some of the unique characteristics of the medium, curator Richard McCabe has assembled one of the most fascinating exhibitions of photography to be seen in New Orleans this year.

As revolutionary as Polaroid Corp. founder Edwin Land’s invention was when it debuted in 1949, McCabe reminds us that it had something in common with the earliest of photographic processes.

“Like tintypes and Daguerreotypes, instant photography produced a singular unique photo-object,” he said.

Yet at the same time, there’s something about Land’s invention that still feels intrinsically modern.

“Instant photography predates digital photography by 40 years, yet it shares a central component of the digital experience: the ability to view the photographic image almost immediately after it is made,” McCabe said.

For all of its modernity, however, instant photography was never treated with the same kind of respect accorded to darkroom processes, perhaps because it was seen as more of a “party trick” than a serious artistic tool.

To his credit, McCabe is successful in redressing that imbalance in the works that comprise “Self Processing.”

There are some big names represented by small pieces in the show, like Andy Warhol’s 1975 portrait of New Orleans artist Tina Freeman — a small-scale reminder of the outsized importance Polaroids had in the pop-art superstar’s ouevre. (An example of the same type of Polaroid camera that Warhol used is displayed nearby.)

And a deeply saturated if otherwise unassuming (and uncharacteristic) botanical study by Sally Mann and two 1980s prints by New Orleans’ own Richard Sexton provide glimpses at the early careers of artists who would become better known for larger and more ambitious bodies of work.

But it’s lesser-known artists in the show who provide some of its most memorable moments.

Michael Meads’ studies of young Southern men somehow manage to combine the monumental light and shadow of Caravaggio portraits with the intimate scale and clandestine, erotically tinged appeal of vintage physique magazines.

Precisely-staged tableaus by Anna Tomczak and Linda Burgess are reminders that instant photography (and its relatively expensive film stock) was conducive to a certain type of meticulousness, reflected in particularly close attention to color, light and composition.

Other artists in “Self Processing” use instant photographs as the basis for different kinds of image making.

John Reuter scrapes away and paints over the various emulsion layers of instant prints to create quietly mysterious and vaguely sinister dreamscapes, while George Blakely’s layering of actual Polaroids found at Disneyland during the 1970s on top of conventionally printed and enlarged copies of themselves result in simple collages rich in memory and association.

The ability of instant photography to capture memory in its own distinctive way also plays a part in a piece by Kathleen Robbins displaying a series of lyrical images taken by her grandmother in the 1980s, which in turn influenced Robbins’ own photographs of life in the Mississippi Delta.

A large grid of Fujifilm instant prints by John Messinger was created by photographing images on computer monitors, creating levels of representation that blur the distinction between analog and digital photography.

Another grid of images by Lisa McCarty chronicles the three-year development of instant film stock by The Impossible Project, so named because it accomplished the “impossible” by resurrecting classic Polaroid-type film after the company discontinued it in 2008. Early images in the series consist of little more than undifferentiated masses of muddy pigment, illustrating Edwin Land’s observation that “An essential aspect of creativity is not being afraid to fail.”

That said, there are a lot more successes than failures in “Self Processing.” Don’t miss it.