Preliminary explanation of the Sleep Fragmentation Index (SFI).
Sleep Fragmentation is an index of restlessness during the sleep period expressed as a percentage.  The higher the index, the more sleep is disrupted. 
The original fragmentation index (FI) was measured in PSG as the number of changes from deep sleep to sleep stage 1 (light sleep) divided by all sleep time (in hours) times 100, resulting in a percentage of total sleep time (TTS). FI is usually accompanied by relatively fast movement lasting between 1 and 3 seconds, which are also called micro arousals. 
In relation to actigraphy, a Belgium study written in December of 1986 (revised 4/6/1987  ) compared data from a device called Actometer with PSG data to determine FI and the following indexes: a movement index (MI), a fragmentation index (FI), and a global index (MFI).
The movement index (MI) was”…obtained by dividing the number of minutes with one or more movements by TIB (time in bed) and multiplying that by 100.” 
The fragmentation index (FI) was determined to be “…the ratio of the number of phases of 1-min. immobility to the total number of immobility phases of all durations multiplied by 100.”  Or “…the number of times that sleep was terminated after 1 minute expressed as a percentage of total estimated sleep time.” 
‘Phases’ from the paper correlate to epochs since they are using 1-min. as a reference time.
“The global index (MFI) is obtained by adding MI and FI…” This is the SFI , as it includes both restlessness and fragmentation of the sleep period. 
The Actiwear® software from Respironics® includes sleep fragmentation as: “((number of mobile epochs lasting four epochs + number of immobile epochs < 1 minute duration / number of immobile epochs > 1 minute duration) x 100)”3, with data recorded at 1-minute epochs.
Movement Index (MI) – The total of scored awake minutes divided by Total time in bed in hours x 100
Fragmentation Index (FI) – The total of 1 minute scored sleep bouts divided by the total number of sleep bouts of any length x 100
Sleep Fragmentation Index (SFI) – The sum of MI and FI.
1 G. Aubert-Tulkens, et al, Ambulatory Evaluation of Sleep Disturbance and Therapeutic Effects in Sleep Apnea Syndrome by Wrist Activity Monitoring, AM REV RESPIR DIS 1987
2 Gueuning F, Eugene C., A long-term microprocessor-bases wrist-worn actimeter, (abstract) Padova: ISAM, 1985: 707-12 (Note: first know battery operated Actigraph).
3 Elizabeth J. Mezick, et al, Intra-Individual Variability in Sleep Duration and Fragmentation: Associations with Stress, 10.1016/psyneuen 2009.04.005
4 Andrea Loewen, et al, Sleep Distrution in Patients with Sleep Apnea and End-Stage Renal Disease, J Clin Sleep Med. 2009 August 15; 5(4): 324-329
5Mary J. Morrell, et al, Sleep Fragmentation, Awake Blood Pressure, and Sleep-Disordered Breathing in a Population-based Study, American Journal of Respiratory and Critical Care Medicine. Vol. 162, No.6 (2000), pp 2091-2026,
6Kristen L. Knutson, et al, Cross-Sectional Associations Between Measures of Sleep and Markers of Glucose Metabolism Among Subjects With and Without Diabetes, Diabetes Care 34:1171-1176, 2011.