https://www.digikey.com/scripts/DkSearch/dksus.dll?WT.z_header=search_go&lang=en&keywords=TSAL6200&x=-1055&y=-51&cur=USDCoin cell has far too high ESR to drive IR LEDs' . As Thickness or length of cell increases, ESR decreases. YOu can verify this with pulse short circuit current.
If you get 1Amp then ESR is 1.5 Ohm , if only if SC current is only 100mA then ESR is 15 Ohms which is the max you should consider but still not as good as Alkaline 1.5V cell which have an ESR of < few ohms.
Small Coin cells have an ESR of > 1kOhm, whereas Alkaline AA cell 1.5V is enough to drive 1 IR LED with ESR of a few ohms. Lithium cell of 2V needs 1- ohm series resistor added as ESR is << 1 Ohm.
IR LED has a threshold of 1V and rises to 1.4 to 1.8V at 100mA max meaning ESR can vary from 4 to 8 OHm depending on device. Consult your specs using VI curve.
Never drive IR LED direct from 5V unless you use 2 or 3 IR LED's in series with R series chosen according to driver drop voltage and power source ESR.
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If you want to match performance of receiver then your emitter needs to match test spec .
IR diode TSAL6200, IF= 0.4 A, 30 pulses, f = f0, t = 10 ms
If you want to drive 0.4A you must ensure pulse duration of modulated frequency is short. The curve increases ESR after 100mA to 400mA. See spec sheet Figure 4