When Woody Allen awoke in the 22d century in "Sleeper," he locked his thickly-bespectacled eyes on those of a futuristic physician wearing equally thick glasses.

In this fantasy of tomorrow, "everything had changed except glasses," recalls Soviet eye surgeon Dr. Svyatoslav N. Fyodorov, who saw the film during a visit to the United States. "I said to myself, 'What can I do to change this?' "

Further inspired by the improved vision of a boy whose corneas were accidentally cut with broken glass, Fyodorov revived and improved in 1974 a surgical technique -- first described nearly a century ago by a German physician -- that corrects nearsightedness.

Called radial keratotomy or RK, the surgery reshapes the cornea with tiny cuts that ultimately bring the world into focus. Although nearly 63,000 Americans have undergone the procedure since 1978, the technique has remained controversial. Preliminary results of the first national study to evaluate RK were released last week at the American Academy of Ophthalmology meeting in Atlanta. Nearsightedness was reduced in the majority of patients, researchers concluded, although serious questions remain.

RK is just one of several surgeries -- still in the experimental stage -- that could make glasses rare by the 21st century. Two newer, unproven surgeries -- epikeratophakia and keratophakia -- appear to correct nearsightedness, farsightedness and astigmatism. But "none have received the consensus among ophthalmologists that they are adequate replacements for glasses or contacts," says Dr. George O. Waring III, a professor of ophthalmology at Emory University and director of the Prospective Evaluation of Radial Keratotomy (PERK) study. "Could they in the future? Of course, if we get good enough at them."

Currently, radial keratotomy is the only one of these surgeries available. In RK, the surgeon makes eight to 16 slices in the cornea -- a clear, dime-sized covering about as thick as a credit card -- that radiate out from the pupil like the spokes of a wheel. These cuts weaken the cornea so its edges bulge and the center flattens to refocus the light. The surgery takes about 15 minutes, can be done in a doctor's office and requires only a few days for the eye to recover.

The first results from the PERK study, a five-year, $2.5 million evaluation of the procedure, concluded that RK appears to be relatively safe in the short term and reduces nearsightedness in most people studied. Of the 413 people who had one eye operated on, RK gave 20/40 vision -- the sight needed to get a driver's license without corrective lenses -- 78 percent of the time.

RK, however, is far from perfect. Although in every case myopia was reduced, 30 percent of the patients had their vision undercorrected and remained nearsighted, and 10 percent were overcorrected and became farsighted.

"The outcome of RK ," cautions Waring, "cannot be precisely predicted for an individual patient." In addition to these problems, astigmatisms developed in 10 percent of patients, 13 percent lost the ability to read one or two lines on the eye chart even with glasses and nearly half experienced glare from the surgical scars.

And in half the patients, vision continued to change more than a year after surgery. "We don't know when it will stop," says Waring.

Despite the risks, 71 percent of the people studied were willing to have their corneas cut in an experimental procedure just so they would not have to depend on corrective lenses.

The two other experimental surgeries that may one day free the 120 million Americans who wear corrective lenses, may solve problems RK can't -- including farsightedness and astigmatisms. They also may be reversible; RK is not.

In epikeratophakia, a technique developed at Louisiana State University in 1979, a button-shaped piece of human cornea is sewn onto the surface of the eye and acts just like a permanent contact lens.

LSU technicians freeze a piece of cadaver cornea and grind it on a lathe to a predetermined corrective power. Once the tissue has been shaped, it is thawed and sewn onto the eye.

If the newly-sewn cornea fails to correct the problem, the surgeon removes it and replaces it with another one, says Dr. Herbert E. Kaufman, director of the LSU Eye Center in New Orleans and one of the researchers developing this approach.

Epikeratophakia "would not be used for trivial myopia," Kaufman says. It would be reserved for people who are extremely nearsighted and now must wear thick glasses that distort their vision.

In the last five years, between 400 and 500 Americans have received this surgery, says Kaufman, who calls it "clearly very effective."

But there are problems. Grinding the frozen corneas into a contact lens is extremely difficult, and at the moment, only LSU has the facilities to do it.

The supply of donor cornea also could become a problem, though Kaufman says that "there seems to be enough tissue."

A third surgical approach, called keratophakia, sandwiches a thin layer of soft, pliable plastic into the middle of the cornea like icing between two halves of an Oreo cookie. The inserted material changes the shape of the cornea to refocus the light and correct vision.

The implanted material, called a hydrogel, consists of the same chemicals found in extended-wear contact lenses. And like contacts, says Dr. Theodore P. Werblin, a practicing ophthalmologist who also does research at the Blaydes Foundation in Bluefield, W.Va., hydrogels should give predictable correction because they can be precisely ground on a machine.

Werblin has begun animal tests of hydrogel implants as have LSU and Emory. No humans have received the implant in the United States, although the surgery has been done on less than 100 people in South America and Europe.

Besides offering a known amount of correction, hydrogel implants theoretically will be reversible, says Werblin.

Keratophakia has technical drawbacks, too. "Just shaving the cornea in half is tricky," says LSU's Kaufman. And after evenly splitting the cornea, the surgeon must evenly insert the hydrogel, and then sew down the flap of cornea.

"We are talking about fractions of a millimeter of curvature," says Dr. Bernard McCarey, associate professor of ophthalmology at Emory University School of Medicine. "It is easy to be off."

Even if these surgeries succeed in focusing vision, they can't completely eliminate glasses. Virtually everyone, starting at about age 45, develops presbyopia -- a form of farsightedness caused by age-related eye changes that make millions of older people use reading glasses.

"In fact, RK aggravates presbyopia," says Waring.

Regardless of success or failure, some scientists worry about whether doctors should even be cutting into a healthy eye that sees perfectly well with corrective lenses.

"About 100 million people in the U.S. need correction, but only 12 percent of them wear contact lenses," McCarey notes. "They don't wear them because contacts are not perfect. We are talking about fancy surgeries when we haven't even mastered contact lenses yet."