There is a simple to use selection guide.

Integrating Sphere Theory
Integrating spheres are used when we have divergent light sources. As shown in the illustration, an integrating sphere has its inner surface coated with a surface that highly reflects (typically 99%) in a scattering, nonspecular way. Thus when a divergent beam hits the walls of the integrating sphere, the light is reflected and scattered many times until the light hitting any place on the walls of the sphere has the same intensity. 

A detector placed in the sphere thus gets the same intensity as anywhere else and the power the detector detects is thus proportional to the total incident power independent of the beam divergence. (The detector is so arranged that it only sees scattered light and not the incident beam). An ideal integrating sphere has a surface with reflective properties are Lambertian. This means that light incident on the surface is scattered uniformly in all directions in the 2pi steradians solid angle above the surface. The surface used by Ophir closely approximates a Lambertian surface.

Step 1 – Starting position

3A-IS Series
The 3A-IS series has two 50mm integrating spheres in series with a photodiode detector. The two series spheres scramble up the light very well thus giving output very independent of incident beam divergence angle. The two spheres in series also insure that the light hitting the detector is greatly reduced in intensity thus allowing use up to 3 Watts even though photodiodes saturate at about 1mW. There are two models, the 3A-IS with a silicon photodiode for 400 – 1100nm and the 3A-ISIRG with an InGaAs detector for 800 – 1700nm

All Ophir power meters, including photodiode power meters, have an air gap between the fiber tip and the sensor. Therefore they measure the power emitted by the fiber into the air and do not take into account any reflection losses there are in the fiber. Therefore, if in actual use, the fiber will be coupled with no loss to another element, then the losses should be added to the reading. These losses are usually about 4%. Thus if the reading on the Ophir meter is say 100 mW, then in lossless use, the real power will be 104 mW.

The Ophir integrating sphere sensors, models 3A-IS and 3A-IS-IRG have a white diffuse reflecting coating on the inside of the integrating sphere. The sensitivity of the sensor is quite sensitive to the reflectivity of the coating. If the coating absorption goes up 1%, it can cause a 5% change in reading. Therefore, care must be taken not to soil or damage the white coating of the sensors. Also it may be a good idea to send the sensors for recalibration yearly.

An unused port should be closed, to prevent unwanted light from entering the sphere. Closing it with a diffuse white port plug, however, adds the surface area of that plug to the (diffuse white) effective area of the sphere that is doing the “integrating”. For a calibrated integrating sphere sensor, this change in the behavior of the sphere changes its calibration, and results in incorrect readings. In such applications, a black “Port Cover” should be used.

Unless otherwise indicated, Ophir sensors and meters should be recalibrated within 18 months after initial purchase, and then once a year after that.

Here is a trick that would make this possible:
The beam should be aimed so that it is incident close to the detector port (but not hitting the baffle) – as shown in this drawing:

This way the "first bounce" will be directed to the opposite side of the sphere, ensuring that the detector will in fact see only light from the "second bounce" and onward, i.e. light that has been uniformly distributed around the inner sphere surface (normally, light from the "first bounce" of a collimated beam is not yet uniformly distributed and we don’t want the detector to see it – that is the main idea behind the different C and D configurations. This trick gets around that).

In general, as the divergence angle of the beam entering the integrating sphere increases - and as its diameter increases – the assumptions on which we base the sphere’s performance (infinite reflections inside the sphere walls, perfectly uniform distribution of light inside the sphere, etc.) become less correct. We therefore specify the maximum beam divergence (such as ± 60⁰), and we also state the maximum possible change in reading caused by change in beam size. In fact, we also state in the data sheet that the maximum additional uncertainty due to beam size is only ±1% for beam divergence < 30⁰, and ±3% for beam divergence > 30⁰. To give this more meaning: Basically, if you measure the power using a beam that is a few mm in diameter, that has a relatively small divergence angle, and is centered on the sphere’s input port aperture, you can safely ignore this additional uncertainty.