Velocity Map Imaging: Understanding 3D Reconstruction

[kelly0303]

Hello! I am a bit confused about the image reconstruction for velocity map imaging. As far as I understand, at the interaction point, ions are produced in a Newton sphere which gets projected on a 2D screen (such that all the particles with the save velocity get mapped on the same point). What confuses me is the reconstruction of the 3D information from this 2D image. From what I read, one needs to do a transformation equivalent to taking a thin slice through the middle of the Newton sphere (e.g inverse-Abel transform). I am not sure I understand why taking a slice through the middle is enough to understand the velocity distribution of the original 3D sphere. If that original distribution has cylindrical symmetry, it would make sense. But is that always the case? If the distribution is not symmetric, a slice through the middle is not representative, right? Can someone help me understand please? Thank you!

 

[sophiecentaur]

Could you help me with a diagram of the apparatus you are describing? Afaik, a "Newton Sphere" behaves according to the Shell Theorem; if it is a conductor then it would not affect the velocity of ions inside it. How does your system separate the ions? How are the ions introduced?

 

[kelly0303]

Could you help me with a diagram of the apparatus you are describing? Afaik, a "Newton Sphere" behaves according to the Shell Theorem; if it is a conductor then it would not affect the velocity of ions inside it. How does your system separate the ions? How are the ions introduced?

Thank you for your reply! Here is a brief introduction and here a more detailed description (there are also many papers in which they built a VMI experimentally, I could suggest some if needed). Basically, by adjusting the potentials between the electrodes, you can make the results of photodissociation (electrons for example) hit the detector at the same point, if they have the same velocity, regardless of where they are produced (assuming the interaction area is not too big, i.e. a few millimeters or less). However in order to reconstruct the original velocity distribution, you need to go from this 2D pattern on the detector to the original 3D one. This can be easily done using an inverse-Abel tranform, but only if the photodissociation products have a cylindrical distribution relative to the place where they were created. This is the case for electrons, but for other ions might not be. So if the original (3D) distribution is not cylindrical, I am not sure I understand why a section to the original Newton sphere (i.e. the expansion of the photodissociation products) still gives the desired answer, as I saw it claimed in several papers, but not explained why. Thank you!