On the infrared scopes that nightly scan the twisted terrain southeast of here, the men, women and children illegally crossing the Mexican border look like pale ghosts against the green-tinted screen.

Often the observer has no patrol available to intercept them. The phantoms pass off his screen, bound for jobs in East Los Angeles or Fresno, eluding the best efforts of Border Patrol statisticians, congressional staffers and university economists to even count them, much less catch them.

The Immigration and Naturalization Service calls them "illegal aliens." The immigration rights groups call them "undocumented workers." The demographers call them "flow."

All would like to know how many of them are successfully crossing the border each year, a crucial point of debate in the wide-ranging immigration legislation approved Wednesday by the House Judiciary Committee. But no one seems to know how to find out.

For 60 years the Immigration and Naturalization Service has been recording the number of persons it catches on the 1,933-mile border between the United States and Mexico. These Mexicans, usually bused right back to the nearest Mexican entry point and let go, are not the problem; the people who escape capture are. But the "apprehensions," as the Border Patrol calls them, provide the only direct clue to the total volume of illegal immigrant flow.

To the distress of INS officials and many western politicians, this apprehension total is about to break all records.

In the fiscal year ending Sept. 30, 1985, the INS totaled 1,183,455 apprehensions at the Mexican border, exceeding even the record year of 1954 when agents raided homes, factories, fields and bars throughout the Southwest in the short-lived "Operation Wetback." This fiscal year, apprehensions are running 43 percent ahead of last year's pace, according to figures provided by INS spokesman Richard Kenney.

If the Mexican border were a laboratory, with all other factors kept constant while the apprehensions rose and fell, it might be possible to estimate how many more Mexicans are successfully entering the country. But the Border Patrol, desperate for resources to make some headway against the tide, has recently succeeded in adding 647 more officers to the force of 1,982 who covered the Mexican border in fiscal 1985. Statisticians note that the 33 percent staff increase will spark a sharp rise in apprehensions even if the illegal border traffic remains steady.

Everyone who has ever interviewed an apprehended Mexican also knows how much the INS figures are swollen by repeat business. A single alien may be caught several times in a year, sometimes more than once on the same day, pushing the annual apprehension total up several notches singlehandedly.

Ask a border patrolman how many aliens are missed for each one captured and the answer usually is, "We get one out of two." But many will then throw up their hands and say, as San Diego sector assistant chief patrol agent Robert C. Gilson did in an interview, "If we said what we really thought, they would think we were completely lying."

In the infrared scopes, Gilson said, an observer can sometimes see groups of 30 go by, too quick or too distant to be captured by patrol officers engrossed in processing the groups they have already apprehended.

One of the few serious studies of successful border-crossers, conducted by UCLA researchers for the Labor Department in 1979, discovered that 69.6 percent of a sample of 1,970 illegal immigrants in Los Angeles had never been previously apprehended. It was an astonishing figure, given the large numbers of often-captured aliens who swell the annual apprehension totals. Cornell University economist Vernon Briggs Jr. said the study "lends credence to the belief" that the illegal inflow "is certainly several multiples" of the INS apprehension figure.

One congressional staff expert said some Texas sectors of the border had shown a recent jump in apprehensions even though they had not yet gotten their new consignment of Border Patrol personnel. Gene R. Smithburg, another assistant chief patrol agent here, said San Diego sector figures show apprehensions this year up 40 to 50 percent, while the number of patrol officers has increased only 30 percent. The difference, he thinks, represents a greatly increased flow as the Mexican economy falters and the California economy booms.

Professional statisticians and immigrant rights advocates treat all Border Patrol figures with skepticism. "Those numbers, who knows how to put any credence in them?" said Susan Drake, staff attorney with the Los Angeles-based National Center for Immigrants' Rights. She cited a family of 15 illegal aliens who returned to Mexico for the funeral of a grandfather, then endured dozens of apprehensions before successfully returning across the border.

Former Census Bureau expert Robert Warren, now INS statistical analysis branch chief, said he distrusts all recent estimates of illegal immigration. Only in hindsight, he said, can he be confident -- through a complex accounting of every Mexican alive in the world -- that there were no more than 2.5 million illegal immigrant Mexicans in the United States in 1980. Although still a large number, this is far below estimates of up to 12 million reported at the time.

Leo Chavez, research associate at the Center for U.S.-Mexican Studies, University of California, San Diego, called apprehension figures "terribly skewed data." Neither American nor Mexican authorities, he noted, try to count the thousands of illegal immigrants known to return to Mexico each year, making it even more difficult to estimate the net flow into the United States.

Estimates of the net annual inflow today range widely. Chavez suggests 200,000 to 250,000. Patrick Burns, research director of the Federation for American Immigration Reform, estimates 500,000 to 600,000. And INS officials usually refuse even to hazard a guess.

But critics of INS statistics are willing to con ede that at the very least, the inflow is increasing. "When you look at the Mexican economy," Drake said, "there is absolutely no question that the push pressures are a lot stronger. The free fall of the economy has pushed out not only the lower classes but the middle class. It is also clear that we have a lot of jobs to fill."