Revenue - Business Revenue (Details) - USD ($) $ in Millions	3 Months Ended								12 Months Ended
	Sep. 28, 2019	Jun. 29, 2019	Mar. 30, 2019	Dec. 29, 2018	Sep. 29, 2018	Jun. 30, 2018	Mar. 31, 2018	Dec. 30, 2017	Sep. 28, 2019	Sep. 29, 2018	Sep. 30, 2017
Disaggregation of Revenue [Line Items]
Revenues	$ 865.8	$ 852.4	$ 818.4	$ 830.7	$ 813.5	$ 824.0	$ 789.3	$ 791.1	$ 3,367.3	$ 3,217.9	$ 3,058.8
United States
Disaggregation of Revenue [Line Items]
Revenues									2,536.0	2,417.6	2,374.8
International
Disaggregation of Revenue [Line Items]
Revenues									831.3	800.3	684.0
Diagnostics
Disaggregation of Revenue [Line Items]
Revenues									1,205.5	1,147.4	1,197.1
Diagnostics | United States
Disaggregation of Revenue [Line Items]
Revenues									921.3	881.6	919.2
Diagnostics | International
Disaggregation of Revenue [Line Items]
Revenues									284.2	265.8	277.9
Diagnostics | Cytology & Perinatal
Disaggregation of Revenue [Line Items]
Revenues									472.0	480.3	477.1
Diagnostics | Cytology & Perinatal | United States
Disaggregation of Revenue [Line Items]
Revenues									312.9	322.9	329.3
Diagnostics | Cytology & Perinatal | International
Disaggregation of Revenue [Line Items]
Revenues									159.1	157.4	147.8
Diagnostics | Molecular Diagnostics
Disaggregation of Revenue [Line Items]
Revenues									675.0	611.8	579.5
Diagnostics | Molecular Diagnostics | United States
Disaggregation of Revenue [Line Items]
Revenues									549.9	503.4	490.9
Diagnostics | Molecular Diagnostics | International
Disaggregation of Revenue [Line Items]
Revenues									125.1	108.4	88.6
Diagnostics | Blood Screening
Disaggregation of Revenue [Line Items]
Revenues									58.5	55.3	140.5
Diagnostics | Blood Screening | United States
Disaggregation of Revenue [Line Items]
Revenues									58.5	55.3	99.0
Diagnostics | Blood Screening | International
Disaggregation of Revenue [Line Items]
Revenues									0.0	0.0	41.5
Breast Health
Disaggregation of Revenue [Line Items]
Revenues									1,314.2	1,218.2	1,138.3
Breast Health | United States
Disaggregation of Revenue [Line Items]
Revenues									1,037.9	951.4	930.1
Breast Health | International
Disaggregation of Revenue [Line Items]
Revenues									276.3	266.8	208.2
Breast Health | Breast Imaging
Disaggregation of Revenue [Line Items]
Revenues									1,094.6	1,016.5	962.2
Breast Health | Breast Imaging | United States
Disaggregation of Revenue [Line Items]
Revenues									853.1	782.0	777.5
Breast Health | Breast Imaging | International
Disaggregation of Revenue [Line Items]
Revenues									241.5	234.5	184.7
Breast Health | Interventional Breast Solutions
Disaggregation of Revenue [Line Items]
Revenues									219.6	201.7	176.1
Breast Health | Interventional Breast Solutions | United States
Disaggregation of Revenue [Line Items]
Revenues									184.8	169.4	152.6
Breast Health | Interventional Breast Solutions | International
Disaggregation of Revenue [Line Items]
Revenues									34.8	32.3	23.5
Medical Aesthetics
Disaggregation of Revenue [Line Items]
Revenues									315.6	339.1	207.5
Medical Aesthetics | United States
Disaggregation of Revenue [Line Items]
Revenues									155.4	172.4	103.0
Medical Aesthetics | International
Disaggregation of Revenue [Line Items]
Revenues									160.2	166.7	104.5
GYN Surgical
Disaggregation of Revenue [Line Items]
Revenues									437.2	422.0	427.1
GYN Surgical | United States
Disaggregation of Revenue [Line Items]
Revenues									362.8	352.8	367.2
GYN Surgical | International
Disaggregation of Revenue [Line Items]
Revenues									74.4	69.2	59.9
Skeletal Health
Disaggregation of Revenue [Line Items]
Revenues									94.8	91.2	88.8
Skeletal Health | United States
Disaggregation of Revenue [Line Items]
Revenues									58.6	59.4	55.3
Skeletal Health | International
Disaggregation of Revenue [Line Items]
Revenues									$ 36.2	$ 31.8	$ 33.5