The effect you are describing in your question is known as wave-particle duality and is a form of complementarity, it has been observed in various experiments. Realisations of Wheelers delayed choice thought experiment are what I find most interesting.
In a delayed choice experiment the particles are not measured before they go through the slits but labeled so which slit they go through is known. The only time a quantum system is not disturbed by a measurement is when no new information is gained from the measurement, labeling ensures which slit the particle went through can be known without disturbing the quantum interference$^1$ of the wavefunction. In this context the purpose of any measurement would be to tell which slit a particle went through anyway.
If a particle has a label when it is detected (at the screen) there is no interference and particle-like behavior is observed. If there are no labels there is interference or wave-like behavior, even if the labels are erased after the particles pass through the slits and it cannot be known which slit they passed through.
It appears that it is not possible to see interference and know which way the particles have gone simultaneously. If there is some which way information that enables a better than blind guess at which slit the particles went through the visibility of the interference is reduced.
However, observation of wave-particle duality does not really require wavefunction collapse. Has wavefunction collapse been observed? In my opinion no, but the publicists for this Nature paper disagree. Collapse is connected to interpretations of quantum mechanics.
Collapse of the wave function would imply that the wave function is real (ontic) as opposed to only representing what we know about a quantum system (epistemic). This is an open question, some physicists think one some the other. There is no experimental evidence either way yet, until there is some physicists might say "Collapse? Ontic? Epistemic? that's all about interpretation, shut up and calculate"
If the wavefunction is purely epistemic then there is nothing real to collapse, only the state of knowledge. If it's ontic then wave function collapse would be a possibility, but even then wavefunction collapse is not required to explain quantum measurement.
$^1$Interference is like the pattern on the left in your question, the wave-like behavior.