The fluorescence microscope

To detect the electron spin resonance frequencies of the NV centers we use a fluorescence microscope, sketched in the figure.

A green laser is reflected off a dichroic mirror and focused into the diamond by a microscope objective, thereby exciting NV centers in the diamond. The resulting NV center photoluminescence is collected by the same microscope objective, transmitted through the dichroic mirror and focused onto the sensor chip of an CMOS camera.

A microwave source generates a microwave current that is delivered to the NV centers by a wire placed on top of the diamond surface, creating the oscillating magnetic fields to drive the NV spin transitions.

Exercise 4 - Calculating the magnetic field of a cylindrical magnet

We apply a magnetic field using a small cylindrical magnet on a translation stage. This magnet has a magnetization $M_s= 0.955 \cdot 10^6$ A/m, a length $L=20$ mm, and a diameter $d=10$ mm.

1. Derive an expression for the magnetic field of this magnet along a line through its axis as a function of the distance $z$ to its center.