Revenue - Business Revenue (Details) - USD ($) $ in Millions	3 Months Ended		6 Months Ended
	Mar. 30, 2019	Mar. 31, 2018	Mar. 30, 2019	Mar. 31, 2018
Disaggregation of Revenue [Line Items]
Revenues	$ 818.4	$ 789.3	$ 1,649.1	$ 1,580.4
United States
Disaggregation of Revenue [Line Items]
Revenues	615.5	588.5	1,237.2	1,185.8
International
Disaggregation of Revenue [Line Items]
Revenues	202.9	200.8	411.9	394.6
Diagnostics
Disaggregation of Revenue [Line Items]
Revenues	296.7	279.7	593.3	564.3
Diagnostics | United States
Disaggregation of Revenue [Line Items]
Revenues	226.8	213.5	454.3	434.7
Diagnostics | International
Disaggregation of Revenue [Line Items]
Revenues	69.9	66.2	139.0	129.6
Diagnostics | Cytology & Perinatal
Disaggregation of Revenue [Line Items]
Revenues	115.5	117.7	233.6	241.1
Diagnostics | Cytology & Perinatal | United States
Disaggregation of Revenue [Line Items]
Revenues	76.6	78.5	155.8	163.2
Diagnostics | Cytology & Perinatal | International
Disaggregation of Revenue [Line Items]
Revenues	38.9	39.2	77.8	77.9
Diagnostics | Molecular Diagnostics
Disaggregation of Revenue [Line Items]
Revenues	167.8	150.7	332.1	299.3
Diagnostics | Molecular Diagnostics | United States
Disaggregation of Revenue [Line Items]
Revenues	136.8	123.7	270.9	247.6
Diagnostics | Molecular Diagnostics | International
Disaggregation of Revenue [Line Items]
Revenues	31.0	27.0	61.2	51.7
Diagnostics | Blood Screening
Disaggregation of Revenue [Line Items]
Revenues	13.4	11.3	27.6	23.9
Diagnostics | Blood Screening | United States
Disaggregation of Revenue [Line Items]
Revenues	13.4	11.3	27.6	23.9
Diagnostics | Blood Screening | International
Disaggregation of Revenue [Line Items]
Revenues	0.0	0.0	0.0	0.0
Breast Health
Disaggregation of Revenue [Line Items]
Revenues	321.5	300.1	646.2	588.1
Breast Health | United States
Disaggregation of Revenue [Line Items]
Revenues	253.0	232.5	505.6	456.9
Breast Health | International
Disaggregation of Revenue [Line Items]
Revenues	68.5	67.6	140.6	131.2
Breast Health | Breast Imaging
Disaggregation of Revenue [Line Items]
Revenues	265.9	250.4	535.6	486.3
Breast Health | Breast Imaging | United States
Disaggregation of Revenue [Line Items]
Revenues	206.2	191.7	412.7	371.5
Breast Health | Breast Imaging | International
Disaggregation of Revenue [Line Items]
Revenues	59.7	58.7	122.9	114.8
Breast Health | Interventional Breast Solutions
Disaggregation of Revenue [Line Items]
Revenues	55.6	49.7	110.6	101.8
Breast Health | Interventional Breast Solutions | United States
Disaggregation of Revenue [Line Items]
Revenues	46.8	40.8	92.9	85.4
Breast Health | Interventional Breast Solutions | International
Disaggregation of Revenue [Line Items]
Revenues	8.8	8.9	17.7	16.4
Medical Aesthetics
Disaggregation of Revenue [Line Items]
Revenues	73.8	85.5	153.6	176.8
Medical Aesthetics | United States
Disaggregation of Revenue [Line Items]
Revenues	37.6	44.4	74.9	91.0
Medical Aesthetics | International
Disaggregation of Revenue [Line Items]
Revenues	36.2	41.1	78.7	85.8
GYN Surgical
Disaggregation of Revenue [Line Items]
Revenues	102.2	99.4	210.6	206.9
GYN Surgical | United States
Disaggregation of Revenue [Line Items]
Revenues	84.1	82.4	175.2	173.9
GYN Surgical | International
Disaggregation of Revenue [Line Items]
Revenues	18.1	17.0	35.4	33.0
Skeletal Health
Disaggregation of Revenue [Line Items]
Revenues	24.2	24.6	45.4	44.3
Skeletal Health | United States
Disaggregation of Revenue [Line Items]
Revenues	14.0	15.7	27.2	29.3
Skeletal Health | International
Disaggregation of Revenue [Line Items]
Revenues	$ 10.2	$ 8.9	$ 18.2	$ 15.0