The surface emitting the photons detected at an arrival time difference , measured from the arrival of the first photon, is not trivially the spherical surface of the fireball at a fixed time difference t , measured from the initial emission, but photons emitted at different t and at different angles reach the detector at the same time .
P is the point where a generic photon is emitted.
L is the distance of P from the observer. R 0 is defined by . Let a photon be emitted at time t from the point P . Its distance from the observer is L . The time it takes to arrive at the detector is, of course, .