BDM International Inc., a McLean, Va.-based professional services company, posted a 37 percent gain in net income for the second quarter and 41 percent jump for the first half of 1983.

Net earnings for the company, which evaluates weapons test data and designs communications devices, mostly for the federal government, rose to $1.4 million (30 cents per share) in the second quarter from $1 million (23 cents) last year. Profits for the first six months of the year totaled $2.8 million (59 cents), compared with $2 million (44 cents) for the same period in 1982.

B. F. Saul Real Estate Investment Trust, Scope Inc. and Digital Systems Corp. also reported higher earnings while, Isomet posted a drop in net income.

B. F. Saul REIT's profits in the third quarter grew to $1.3 million (21 cents), compared with last year's $557,000 (9 cents). Earnings of $7.3 million ($1.22) for the first nine months of 1983 showed a complete turnaround from a loss of $4 million (67 cents) for the same period in 1982.

Scope also turned around losses in its second quarter and first six months last year into gains this year. The company posted net income of $409,000 (33 cents) in the second quarter, compared with last year's loss of 273,000 (22 cents). The company also reported a gain in net earnings of $230,000 (19 cents) for the first six months of this year, compared with last year's loss of $663,000 (55 cents).

Isomet's second-quarter earnings fell to $30,000 (2 cents), down from $84,000 (5 cents) for the same period in 1982. Net income of $52,000 (3 cents) for the first six months of this year was also substantially lower than last year's $247,000 (16 cents).

Profits for Digital Systems nearly tripled in the past year, the company reported. Earnings for the first nine months of its 1983 fiscal year, which ended June 30, climbed to $940,000 (43 cents), up from last year's $335,000 (15 cents).

The higher profits at Digital Systems are due primarily to revenues from the company's contract with the Navy's underseas surveillance command, a company spokesman said.