Cmdr. Donal M. Billig, the former heart surgeon at Bethesda Naval Hospital who has been charged in four deaths there, applied to the Navy a week after Air Force recruiters in Pittsburgh told him that a physical examination showed his eyesight to be "unacceptable," according to Air Force personnel and Navy documents.

Billig, who had been a staff physician for five hospitals in the Pittsburgh area, underwent a physical examination on Aug. 11, 1982, by Dr. William Ryckman, a family practice physician who is under contract to the Air Force. Ryckman said he conducted four eye tests -- including those for depth perception and visual acuity -- and Billig's right eye failed all four.

"Two of the tests were the kind you use to test for what we call 'lazy eye,' " Ryc- kman said yesterday. "His right eye was so lazy that it didn't move at all.

"I asked him: 'How in the heck can you be a surgeon when your depth perception is so bad?' He said, 'Well, you learn how to adapt . . . .' I told him I didn't think there was any way he could get in with that eye problem."

Billig, 54, faces a court-martial on charges of involuntary manslaughter in connection with the deaths of four patients at Bethesda Naval Hospital and 28 charges of dereliction of duty for operating without proper supervision. Neither he nor his attorney could be reached for comment yesterday.

Ten other Navy officers -- including recruiters, the former commanding officer and executive officers at Bethesda -- face disciplinary sanctions in connection with the hiring of Billig.

Navy spokesmen said yesterday that "information regarding Billig's Air Force physical was received during the recruiting process" but they would not elaborate on what information that was. Air Force spokesmen said that "data was provided to the Navy" about Billig but could not determine what data because records no longer exist.

Ryckman said yesterday he had been told by Navy investigators two months ago that the Navy had found a family medical history from the Air Force in their files on Billig but did not have a record of the physical exam he completed.

Billig, who was required to have a physical exam once a year while in the service, did not have one in 1983 or 1984, Navy spokesmen said yesterday. Billig worked at Bethesda, the premier hospital for the Navy, from January 1983 through November 1984. His last position was as head of heart and chest surgery.

According to documents obtained under the Freedom of Information Act, Billig was seen in the Pittsburgh Navy recuiting office as a "walk-in candidate" on Aug. 17, six days after the Air Force examination. On Aug. 23, an application completed by Lt. Cmdr. Jerry Penn, one of the officers under investigation because of the recruitment of Billig, indicated the surgeon wore eyeglasses.

Documents also indicate that on Sept. 30, the Navy expected results of the "physical to be sent by the Air Force."

Air Force spokesmen said yesterday that Billig was not rejected by the Air Force but was told he needed to see another doctor. He never followed that up, spokesmen said, and his application was not completed.

Ryckman said yesterday he found Billig's vision in his left eye to be correctable to 20/20 and the vision in his right eye to be correctable to only 20/100.

Navy spokesmen said a recent examination of Billig found his vision in his right eye could be corrected only to 20/400, a level that Ryckman said yesterday would make the heart surgeon legally blind in that eye.

Ryckman said Billig told him that his eyesight had been damaged years ago when he was a young boy, and a tennis ball hit him. In court documents submitted by Billig in 1980 in the state of New Jersey, however, Billig said he had suffered an injury to his eye "approximately a year-and-a-half ago." Those documents were filed by Billig after he was asked to leave Monmouth Medical Center based on competency questions.

Spokesmen from Montifiore, Jefferson, Central Medical, Braddock and Monangahela hospitals in Pittsburgh have confirmed Billig was on their hospital staffs, but would not elaborate on his work.

One former associate of Billig's, Dr. Chit Phitayakorn, said yesterday Billig was asked to leave Thoracovascular Associates. Phitayakorn, a heart and chest surgeon no longer with that medical group, would not elaborate.

Two other doctors still associated with the group, Drs. Manfred L. Cohen and David M. Long, previously refused to discuss Billig, although Navy documents show that Cohen recommended Billig on Aug. 25, 1982, as "most satisfactory."