I understand that a hollow-cathode lamp (HCL) with a specific target is used to excite the sample. The atoms in the sample absorbs the photons and re-emits at the same wavelength and the signals are measured by the detector.
What about the signal from the source? Let's say only 20% of the energy from the source are being absorbed, wouldn't the other 80% also travel through the flame to the detector?
You raised an excellent point, which is not as simple a UV-Vis spectrophotometry because most molecules do no fluoresce or emit light, whereas atoms do. This issue makes an atomic absorption experiment slightly more challenging (at least in principle). The critical question is "what" signal reaches the detector. How does one distinguish the contribution of flame emission from the hollow cathode lamp (HCL) beam? Last but not least, is there is a way to distinguish atomic emission due to HCL?
Have a look at a typical AAS instrument. The critical component is the chopper, which is nothing but a rotating mirror with holes. It merely blocks the light from reaching the flame while rotating at an exact frequency.
You can see only two signals are needed in an atomic absorption spectrophotometry experiment: a) Light beam intensity when there are no atoms in the flame and b) light beam intensity when analyte atoms are present in the flame.
You aspirate a blank (no analyte solution) into the flame- this sets the 100% transmission or absorbance = 0 at the chosen wavelength. Ignore the reference beam; it is for ensuring that the lamp is stable. We are only interested in the beam passing through the flame.
Next, you would aspirate your analyte solution into the flame. Let us take Na as the most straightforward example. There is light absorption by Na atoms in the flame, leading to a reduction in the HCL beam's light intensity after passing through the flame. The ratio of light intensity in steps 2 and 1 gives the transmittance, which is easily converted into absorbance.
However, there is an almost continuous emission spectrum from the flame too.
Here is the smart idea. I do not know who came up with it. The detector continuously sees the background emission from the flame. However, the light beam from the hollow cathode lamp reaches the detector alternately at a particular frequency due to the rotating chopper. The electronics are tuned to register only the light, which is oscillating due to the chopper
The good news is that atomic fluorescence is not directional, unlike the light beam from the HCL. Secondly, the intensity of atomic fluorescence light is so small compared to the HCL beam intensity that it is practically negligible. There is no way to prevent atomic fluorescence from reaching the detector in an atomic absorption experiment, to the best of my knowledge.
Can we see stars during daylight? Stars are always there and "part" of the sunlight. However, stars contribute very little to the daylight. In the same way, atomic fluorescence contribution in an atomic absorption experiment is almost null because the hollow cathode lamp beam is quite strong as compared to the atomic fluorescence in random directions.
There is measured the relative portion of the passed, not absorbed, eventually modulated light. It is the same principle as measurement of absorbance of coloured solutions by classical UV/VIS spectrometer.
$$I = I_0 \cdot 10^{-A} = I_0 \cdot 10^{-\epsilon \cdot c \cdot l}$$
The difference is the atomic absorption bands are very narrow and intense, so measurement is very selective and sensitive.
Re-emission or fluorescence occurs, but as it is omdirectional, it is negligible in directions of the primary ray. Additionally, fluorescence happens at not measured wavelength.
