Fogged in recent weeks by on-camera missteps and now the center of a serious tugging match among senior presidential advisers, Jimmy Carter's electronic image will flicker across the national ether throughout this week in search of public support and understanding.

Today he will be our president the risk-taker, confronting a news conference. Wednesday night he is the serious but friendly president, chatting beside the metaphorical fireside to explain the Panama Canal treaties. At week's end, he goes "soft," in the trade terminology, becoming a ceremonial host and visual national symbol for news coverage of Egyptian President Anwar Sadat's visit.

For much of America, Carter remains surprisingly undefined a year into his presidency. His video images form the most direct contact that many Americans have with the White House. For some, the presidency increasingly is television.

"The presidency has become an ongoing series for television and the enormous amounts of time it has to fill up," says political marketing expert Jerry Rafshoon. "Everybody else goes on taped or like Barbara (Walters) and Walter (Cronkite) with a script on teleprompters, Jimmy Carter is almost alone in doing live, spontaneous television today.

"It is good public policy for Americans to see their leader grilled," says Barry Jagoda, a former television producer who is Carter's electronic media adviser and who is far more adamant than Rafshoon about "exposing the president to risks" through live appearances.

"It is also good television," Jagoda adds. "People watched the spaceshots because they knew each time something might go wrong and the astronauts could be burned up before their eyes. We want that kind of authenticity, that sense of natural vulnerability and of being on top of things."

Rafshoon and Jagoda are members of the small inner circle of White House staffers and Carter intimates directly involved in guarding and projecting the presidential-image. That group has been locked in serious debate in recent weeks over Carter's public persona and its role in Carter's difficulties in getting legislative programs enacted and in defining himself to the public.

As with almost all White House debates, this one involves both the ongoing contest for influence that presidential advisers wage and, ultimately, Carter's re-election strategy for 1980, when new ratings will be taken for the Oval Office series. In each of Carter's television appearances this week, there will be fingerprints of winners and losers in the debate. There will also be hints of how Carter and his chief political operative. Hamilton Jordan, see the electoral scene at the moment.

But the largest fingerprint of all will be that of television, as technology has in a sense become a participant in any White House image debate at the end of the 1970s. Much of the impression viewers carry away will have been largely decided before Carter utters his first word in any of the three settings for this week's performances, the president's medica men agree.

"Television may not be too deep, but it's broad as hell," press secretary Jody Powell said. "When you have a subject like energy that is not chatty, you need something to indicate that this is serious business. We did that with energy. Press conferences are also important because people make judgements based on seeing the president answer questions."

On television "people are less interested in what the president is actually saying," acknowledges the president's chief speech writer, James Fallows, who labored on at least six drafts of the State of the Union Message that Carter himself substantially rewrote. "I would bet that for the public the main impact of the State of the Union Message was the scene, with the President getting lots of applause in an impressive setting"

Today, much of the battle around Carter about Carter has to focus on the vital question of format because of the new importance television attaches to it. A recommendation to the President on how he says something visually goes a long way toward deciding the aurel perception of what he has said, a fact that has not been lost on White House staffers.

A small but significant erosion of confidence in the President's job performance rating measured by recent public opinion polls also frames the insiders' debate in more traditional terms.

The President is also being told to use television and other appearances to govern more effectively, to rally public support and thus halt and reverse the erosion of public confidence.

Ironically, the perils involved in treading televisions highwire have contributed to Carter's recent public perception problems. Since November, Carter has:

Delivered a national address on energy that was declared by some critics to be the worst presidential speech ever made.

Upset Egypt's Sadat with a remark about Palestinian statehood in a yearend interview.

Let India's prime minister know via a television microphone, Carter thought was off that a "cold and very blunt letter" would come his way when Carter got back to Washington.

Stumbled into a credibility dispute with the Washington press corps over his press conference explanation of the firing of the U.S. attorney in Philadelphia, David W. Marston. That dispute could dominate today's regularly scheduled press conference.

Delivered the State of the Union Message, which at least in television terms, sank without a trace. Perception Problems

These missteps and missed opportunities have helped rekindle an argument heard in the early states of the Carter administration about the dangers of "overexposure" and "television burn-out" if Carter went on the air too often. But all indications out of the White House are that Carter has decided that more television, not less, is part of the answer to his perception problems.

"The public is not getting enough clear symbols from the White House," Rafshoon said in an interview in the new Washington office of his Atlanta-based advertising firm. His Washington operation is located two blocks from the White House, which he helped Carter capture with his media advertising campaign in 1976. "Carter doesn't use television enough, especially when he comes up against institutional resistance to his plans."

Carter's decision to return to the White House law library and a crackling fireside for Wednesday night's talk on the Panama Canal represents a boost for Rafshoon's strategy. Reflecting his belief that "all politics is marketing," Rafshoon favors putting Carter in controlled, sympathetic environments and letting him guide the viewing nation through the complexity of issues in a chatty way.

Wednesday night's appearance was in fact forced on Carter by Senate Majority Leader Robert C. Byrd (D-W. Va.), who Thursday told other senators backing the canal treaties that Carter would go on the air at their request, evidently to build public acceptance of the Senate vote. Carter and Jordan Have reportedly now decided to make Wednesday night's appearance the first of an increased number of such informal chats to gain public support for other programs.

Jagoda, who works closely with Powell on televised press conferences and interviews, clearly takes another approach to the presidential image. He proudly agrees that he is in a sense still a television producer who now is working inside the White House, making sure the interests of the networks and of the White House "are in harmony."

"Jimmy Carter is not a school teacher or an anchor man," Jagoda said in an interview before the decision had been made on a new fireside chat. "I don't think we ought to show him in front of blackboards or with meaningless symbols around him. Any symbols the presidents uses have to be believable symbols." Carter Is Low Key

Jagoda, 33, is intense and speaks in kinetic sentences that are verbal equivalents of movie or TV jump cuts. He has turned the adviser's job into a far more important and visible one than his predecessors in the Nixon and Ford administrations, using the title Media Adviser to the President to get a handle on cultural affairs and communications policy.

Critics in the White House staff and in television focus on what they say is Jagoda's abravsiveness, and Powell is quoted as saying he hired Jagoda "because only Barry is obnoxious enough to take care of these obnoxious television people." But even his critics credit Jagoda with having and applying the best understanding of television as a medium of anyone who has ever worked in the White House.

"President Carter has a low-key personality," said Jagoda, who left CBS-TV to join Carter's campaign early in 1976, "and it tends not to be magnified by television the way others can be. The average guy can come across very ebullient. Television helps bring Jimmy Carter up to perceived normalcy."

Jagoda, who helped put together the radio call-in show that boosted Carter in public opinion, would like to see him do "more things like that that are not canned. Traditional politicians insist on control. They don't understand production values. Jimmy Carter's strong suit is candor."

Jagoda and Powell make similar arguments that Carter is safer "making controversial statements on national television than at a news briefing with only six journalists present," as Jagoda says.

Powell makes this assertion about Carter's statements on Marston: "I think the 14 million viewers that day clearly understood the President. The nitpicking comes from the news people, who can't continue to have it both ways. You can't expect anyone to be as accessible and on the record as Jimmy Carter has been and still reserve the right to nitpick every phrase."

Powell, who says the White House would be "just as happy" if the three main commercial networks did not all televise the twice-a-month daytime press conferences, plays the key role in preparing Carter for the press conferences. He assembles documents from the National Security Council and the domestic policy staff into two briefing books and adds to them his own political summaries Performance May Be Crucial

Carter and Powell spend about two hours before a press conference going over the briefing books. Powell said he talked briefly with Carter about a report that Marston was undertaking an investigation that might involve a Democratic congressman, Joshua Eilberg of Pennsylvania, before the Jan. 12 press conference, but that he personally had refused to put anything in writing in the briefing book "because I did not think it was right to cast suspicion on a man that way. That was why the president also did not want to focust attention on an investigation that we were not clear about, and that is why he answered the way he did."

The result was clearly an image setback for Carter, and his performance today may be crucial in either undoing or reinforcing that impression. Carter's advisers agree that Richard M. Nixon's Watergate performances indicate the problems of using television today as a defensive medium.

"You can use opening statements at a press conference to get your concern on the record about something, but they are not short speeches," noted Fallows. His speechwriting team is the most evident loser in the drift back to a more generalized, friendlier and extemporaneous Fireside image of Jimmy Carter, after the President's recent lackluster performances in more formal settings.

"When you have a specific important policy to present, you should have a formal speech. It makes sure that all bases in the policy empire are touched," Fallows continued. "The State of the Union was the first all-encompassing document on both foreign and domestic policies this administration has assembled.

"With that speech, you are trying to get Congress, the press and other specialized audiences to listen to you. That kind of message should be digested in the press and analyzed by newspapers and magazines. It is more complicated and longer than the television talk language," Fallows added. "I think it is really admirable in Carter that his mind doesn't leap to how something will play on television."

Interestingly, Carter's advisers involved with the media all remain convinced that Carter attaches particular importance to each of their differing approaches. Moreover, they make predictable but apparently genuinely felt protests that they in the final analysis can get Carter to do little about his image unless the often aloof private president wants to do it himself.

"His image is very much like his strengths and his weaknesses," Powell said. "Rather quiet, not given to strong statements, sincere and thoughtful. Also, not a rhetorician. That cuts both ways. In the long run, you don't take a man who is 53 years old and make him something he's not."