When a quantum of light arrives at a double slit, it passes through both slits as a wave and arrives upon a second screen with the interference pattern of a single wave that has been split into two waves, that have then interfered with each other.
This is not correct. The photons arrive one at a time whole, not split in space. In any case, in quantum mechanics what is waving is the probability of detecting the particle not the particle itself.
Here is the double slit experiment displaying one photon (quantum of light) at a time, and what happens when many photons are accumulated.
Single-photon camera recording of photons from a double slit illuminated by very weak laser light. Left to right: single frame, superposition of 200, 1’000, and 500’000 frames.
At the frame on the far left the footprints of the individual photons are seen. The photons do not leave a signal all over the place, they hit at a specific (x,y)at a distance z, according to the probability of the solution for the setup "photons scattering off two slits with specific width and distance". This probability is given by the $Ψ*Ψ$ of the specific wavefunction and it looks random in the first frame on the left.
The accumulation of photons shows the classical interference pattern, which for the quantum level means the probability distribution $Ψ*Ψ$.
A detector after one of the slits intercepting the photon, changes the boundary conditions to a different system, and thus a different $Ψ*Ψ$. It is no longer the same experimental setup. It should be obvious that if the detecting instrument after the slit , absorbs the photon like the screen does, only the untouched slit will give a signal on the far screen, which could not interfere with itself .( A sophisticated experiment with electrons which tries to minimally show the effect came to the conclusion that the detecting level acts as a point source for the electrons going through it, i.e. a different $Ψ*Ψ$ for the electron which is no longer coherent so as to show the interference pattern.)
Therefore can one assume that detection has 'caused' the collapse of the wave portion of the duality?
Detection at the screen has picked ("collapsed ")an instance of (x,y,z) of the original wavefunction and removed that photon from the final screen. In general after the detection of "which slit" the photons are in a different wave function with new boundary conditions.
How has detection precisely influenced the duality? Can anyone clarify?
The duality is not affected by detection, the mathematical model that describes the probabilities , $Ψ*Ψ$, has a different Ψ because the boundary conditions have changed and the coherence necessary to display interference is lost.(coherence in the phases describing the photons in spacetime). Again, the term wave particle duality has to do with the mathematics of the quantum mechanical probabilities. The probability is a wave, (a solution of a quantum mechanical system) the particle manifests as a point in (x,y,z,t) when interacting in a measurement, in accumulation of many particles with the same boundary conditions, the probability distribution is built up.(It is the same as throwing dice. The probability distribution versus the numbers 1-6 is seen in the accumulation of many throws).